President Barack Obama and Republican presidential nominee Mitt Romney threw a lot of facts and numbers at each other in Denver Wednesday night — details often so jarringly at odds that the two men seemed to be inhabiting two parallel universes. 
 
 Here’s POLITICO’s guide to sorting through some of the edgiest claims, and what the independent experts off the stage have had to say about what the two candidates claimed: 
 
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 reset 2012 First Presidential Debate in Denver POLITICO's 2012 Presidential Debate Post Game 
 
 (See also: Complete coverage of 2012 presidential debates) 
 
 The $5 Trillion Tax Cut 
 
 Romney: “I’m not looking for a $5 trillion tax cut. … I won’t put in place a tax cut that adds to the deficit. That’s part one. So there’s no economist that can say Mitt Romney’s tax plan adds $5 trillion if I say I will not add to the deficit with my tax plan. ... .I will not reduce the taxes paid by high-income Americans.” 
 
 Obama: “Governor Romney’s central economic plan calls for a $5 trillion tax cut….For 18 months he’s been running on this tax plan. And now, five weeks before the election, he’s saying that his big, bold idea is, ‘Never mind.’” 
 
 (PHOTOS: Scenes from the Denver debate) 
 
 Independent analysts say Romney’s numbers don’t add up. The rate cuts and other changes he’s proposing would indeed total almost $5 trillion over 10 years, and though he said Wednesday he’d pay for those cuts by reducing deductions and credits, a study by the Tax Policy Center found that it was “mathematically impossible” to cover the $5 trillion reduction by eliminating tax breaks solely on high-income taxpayers. 
 
 In an interview earlier this week, Romney said he might cap deductions at $17,000. During the debate, he suggested such a cap might kick in at $25,000 or $50,000. However, it’s not clear how those limits would get around the problem the Tax Policy Center study noted. The Romney camp contends that study is biased and points to others with different results. 
 
 (Also on POLITICO: Romney’s 5 best debate lines) 
 
 Romney acknowledged Wednesday that the bare numbers of his tax plan might not be revenue-neutral, but he said growth and new jobs created by his policies would generate added revenue to cover the gap. 
 
 Simpson-Bowles 
 
 Obama: “We’ve [taken the Simpson-Bowles deficit reduction plan,] made some adjustments to it, and we’re putting it forward before Congress right now, a $4 trillion plan.” 
 
 Obama made the deficit-cutting plan he’s offered sound comparable to the plan from the chairmen of the Simpson-Bowles debt cutting commission. But it’s not: His proposal doesn’t save as much money as Simpson-Bowles and doesn’t offer the kinds of detailed entitlement cuts the panel’s leaders did. 
 
 The president’s $4 trillion plan, including $3 trillion in spending cuts and $1 trillion in tax hikes from allowing the Bush-era tax cuts to expire, is spread over 10 years — a year longer than Simpson-Bowles. It sounds like a minor difference, but cuts and spending balloon in the so-called out years. 
 
 (Also on POLITICO: Obama’s 5 best debate lines) 
 
 Also, Obama doesn’t touch Social Security in his plan. And the tax changes and war spending are accounted in ways that make Obama’s plan substantially less aggressive. 
 
 “The president’s budget falls well short of the savings claimed by the [Simpson-Bowles] commission,” according to the Committee for a Responsible Federal Budget. The committee, the kind of wonky group Obama loves to cite, said Obama’s plan provided only about two-thirds of the savings Simpson-Bowles proposed over a comparable period with comparable assumptions. ||||| But this year, as the line between acceptable political debate and sophistry has often been crossed, the accuracy of campaign statements has emerged as a campaign issue. Here is an examination of some of the claims and counterclaims. 
 
 Doubling the Deficit 
 
 Mr. Romney said Mr. Obama had doubled the deficit. That is not true. When Mr. Obama took office in January 2009, the Congressional Budget Office had already projected that the deficit for fiscal year 2009, which ended Sept. 30 of that year, would be $1.2 trillion. (It ended up as $1.4 trillion.) For fiscal year 2012, which ended last week, the deficit is expected to be $1.1 trillion — just under the level in the year he was inaugurated. Measured as a share of the economy, as economists prefer, the deficit has declined more significantly — from 10.1 percent of the economy’s total output in 2009 to 7.3 percent for 2012. JACKIE CALMES 
 
 The $5 Trillion Tax Cut 
 
 Mr. Obama and Mr. Romney repeatedly sparred over whether Mr. Romney has proposed a $5 trillion tax cut. 
 
 It is true that Mr. Romney has proposed “revenue neutral” tax reform, meaning that he would not expand the deficit. However, he has proposed cutting all marginal tax rates by 20 percent — which would in and of itself cut tax revenue by $5 trillion. 
 
 To make up that revenue, Mr. Romney has said he wants to clear out the underbrush of deductions and loopholes in the tax code. But he has not yet specified how he would do so. 
 
 This week, in a television interview, Mr. Romney did shed some light — floating the idea of capping each household’s deductions at $17,000. 
 
 “As an option, you could say everybody’s going to get up to a $17,000 deduction. And you could use your charitable deduction, your home mortgage deduction, or others, your health care deduction, and you can fill that bucket, if you will, that $17,000 bucket that way,” he said. “Higher-income people might have a lower number.” 
 
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 The deduction cap has the virtue of avoiding the tough negotiations over which tax expenditures to unwind. Many tax expenditures are highly popular, like the deduction for charitable giving. Moreover, many are important to the stability of the economy. Suddenly ending the home mortgage interest deduction, for instance, would threaten to destabilize the housing market. 
 
 But a number of unanswered questions about Mr. Romney’s tax plan remain. 
 
 For instance, Mr. Romney did not address how his proposed cap on deductions would affect tax credits. (Generally, deductions lower a family’s level of taxable income and credits erase part of their overall tax bill.) 
 
 It is also unclear whether his proposal to cap deductions would raise enough revenue to pay for his income tax rate cuts — at least not without increasing the tax burden on families making less than $200,000 a year, which Mr. Romney has vowed that he will not do. ANNIE LOWREY 
 
 Government ‘Takeover’ Of Health Care 
 
 Mr. Romney said that Mr. Obama’s health care overhaul would allow the federal government to “take over health care,” an assertion rejected by the president. 
 
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 The 2010 health care law clearly expands the role of the federal government. But it also builds on the foundation of private health insurance, providing subsidies for millions of low- and moderate-income people to buy private insurance. 
 
 Under the law, close to 30 million Americans are expected to gain health coverage, according to the Congressional Budget Office. Many of them would receive insurance through the expansion of Medicaid. The federal government will initially pay the entire cost of Medicaid coverage for newly eligible beneficiaries and would never pay less than 90 percent. 
 
 In addition, the federal government would subsidize the purchase of private insurance for millions of people with incomes up to four times the poverty level (up to $92,200 for a family of four). Private insurers would thus have many new customers. 
 
 Projections by the nonpartisan office of the actuary at the Department of Health and Human Services show that federal, state and local government health spending will account for nearly 50 percent of all health spending in the United States by 2021, up from 46 percent in 2011. The federal share of all health spending is expected to rise to more than 31 percent, from slightly less than 29 percent. 
 
 The changes reflect the expansion of Medicaid eligibility and the new subsidies for private insurance, as well as the increase in Medicare enrollment as baby boomers join the program. 
 
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 When Mr. Romney and other Republicans complain of a federal takeover, they are referring to more than spending and enrollment in government health programs. They say the new health care law will require most Americans to purchase “government-approved insurance” or pay a new tax. The tax issue was at the heart of the Supreme Court’s much-debated 5-to-4 decision in June to uphold the president’s health care overhaul law, the Affordable Care Act. ROBERT PEAR 
 
 Green Energy 
 
 Mr. Romney said that half the companies backed by the president’s green energy stimulus program have gone out of business. That is a gross overstatement. Of nearly three dozen recipients of loans under the Department of Energy’s loan guarantee program, only three are currently in bankruptcy, although several others are facing financial difficulties. Mr. Romney also said that “many” of the companies that received such loans were supported by campaign contributors. George Kaiser, a major fund-raiser for Mr. Obama’s 2008 campaign, was an investor in Solyndra, the failed solar panel maker, but there are also examples of Republican and Democratic campaign contributors who also invested in firms supported by the loan guarantee program. JOHN M. BRODER 
 
 The $716 Billion Cut From Medicare 
 
 Mr. Obama first brought up Mr. Romney’s frequent criticism that the president cut $716 billion from Medicare, by saying the cost savings were from reduced payments to insurance companies and other health care providers. But Mr. Romney repeated the claim, suggesting that the $716 billion in Medicare reductions would indeed come from current beneficiaries. 
 
 While fact-checkers have repeatedly debunked this claim, it remains a standard attack line for Mr. Romney. 
 
 The charge that Mr. Obama took $716 billion from Medicare recipients to pay for “Obamacare” has several problems — not least the fact that Mr. Romney’s running mate, Representative Paul D. Ryan, included the identical savings in his budget plans that House Republicans voted for in the past two years. 
 
 Mr. Obama did not cut benefits by $716 billion over 10 years as part of his 2010 health care law; rather, he reduced Medicare reimbursements to health care providers, chiefly insurance companies and drug manufacturers. And the law gave Medicare recipients more generous benefits for prescription drugs and free preventive care like mammograms. 
 
 According to nonpartisan analysts, it is Mr. Romney who would both cut benefits and add costs for beneficiaries if he restored the $716 billion in reductions. Restoring higher payments to insurers and other companies would in turn increase Medicare premiums because beneficiaries share in Medicare’s total cost. Marilyn Moon, a vice president at the American Institutes for Research, has calculated that a Medicare recipient’s out-of-pocket expenses would increase $577 a year on average by 2022. 
 
 Also, the Obama reductions added eight years to the life of Medicare’s financially troubled trust fund, to 2024, according to Medicare trustees. If the cuts were restored, the insolvency date would revert to 2016. 
 
 But the cuts to providers could cause private Medicare plans to raise their premiums, which is expected to reduce enrollment in them. Those changes have not materialized yet. 
 
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 JACKIE CALMES ||||| An energetic Mitt Romney launched a series of attacks against President Obama here Wednesday night, calling into question the president’s record on the economy, health care and the deficit, and arguing that he would take the country in a fundamentally different direction. 
 
 Obama sought to parry Romney’s criticisms, charging that his presidential rival favors a top-down approach to the economy that would reward the wealthiest Americans at the expense of the middle class and that the details of the Republican’s proposals don’t add up. But he found himself on the defensive repeatedly during their first debate, held at the University of Denver. 
 
 Romney came into the 90-minute exchange after several difficult weeks but appeared rejuvenated by the opportunity to take his case directly to Obama and the American people. He was well prepared and aggressive as he hammered the president. The contrast with Obama was striking, as the president appeared less energetic even as he rebutted some of Romney’s toughest attacks. 
 
 The debate is likely to give Romney what he needed most, which is a fresh look from voters — at least those who are undecided or open to changing their minds — and will change the conversation about the campaign, which for the past two weeks has been tilted in the president’s favor. Romney now faces the challenge of trying to build on his performance and keep the president on the defensive in the days ahead. 
 
 Romney offered conservative policies throughout the evening but he often sounded more moderate than he does in campaign appearances. He is likely to face a challenge from Obama and the Democrats in the coming days about the contrast in tone and posture on display during the night. 
 
 1 of 23 Full Screen Autoplay Close Skip Ad × Presidential candidates face off in Denver View Photos President Obama and Mitt Romney met for the first of three debates Wednesday night. Caption Domestic policy was the focus of the debate in Denver. Oct. 3, 2012 Republican presidential nominee Mitt Romney shares a laugh with President Obama after finishing up the first presidential debate at the University of Denver. Marvin Joseph/The Washington Post Buy Photo Wait 1 second to continue. 
 
 But Republicans were immediately cheered by the aggressiveness they saw in Romney and took it as a sign that he will wage a fierce battle between now and Nov. 6. 
 
 PBS’s Jim Lehrer moderated the forum, which included a more open format that encouraged a free-flowing discussion, and most of the exchanges focused on the economy, the federal budget deficit and health care. The debate was generally civil and proved to be one of the most substantive and detailed in recent memory. 
 
 The weak economy has long been Obama’s biggest obstacle to reelection. On Wednesday, he argued that, although the country faces problems, it has begun to “fight our way back” because of his policies and the resilience of the American people. 
 
 “Over the last 30 months, we’ve seen 5 million jobs in the private sector created. The auto industry has come roaring back. And housing has begun to rise. But we all know that we’ve still got a lot of work to do. And so the question here tonight is not where we’ve been but where we’re going.” 
 
 But Romney said the status quo “is not going to cut it” for struggling families. “Under the president’s policies, middle-income Americans have been buried. They’re just being crushed. Middle-income Americans have seen their income come down by $4,300. This is a tax in and of itself. I’ll call it the economy tax. It’s been crushing.” 
 
 Romney clearly came to the debate determined to change his image as someone who cares little for ordinary Americans, a view that was heightened by his dismissive comments about the roughly 47 percent of Americans who pay no income taxes. 
 
 Throughout much of the early part of the debate, he sought to portray himself as a protector of the middle class, not the wealthy. He said that he would not raise taxes on middle-class families and that he would not reduce the share of taxes paid by the wealthiest Americans. 
 
 Obama, however, said that Romney’s tax plan would do just that. He said his rival favors a $5 trillion tax cut and argued that eliminating loopholes and deductions for the wealthiest Americans would not provide enough revenue to avoid deepening the deficit. He said Romney would either have to cut into middle-class benefits or reduce spending on vital programs. 
 
 “The magnitude of the tax cuts that you’re talking about, Governor, would end up resulting in severe hardship for people but, more importantly, would not help us grow,” the president said. 
 
 Romney repeatedly has declined to specify what loopholes and deductions he would eliminate and passed up opportunities to do so again Wednesday. But he said Obama had mischaracterized his tax plan, saying that it does not include a $5 trillion cut. 
 
 “Let me repeat what I said,” Romney said. “I’m not in favor of a $5 trillion tax cut. That’s not my plan. My plan is not to put in place any tax cut that will add to the deficit.” 
 
 Obama and Romney clashed over Medicare, with both promising to protect the health-care program for seniors. Obama accused Romney of wanting to turn it into a voucher program, while Romney claimed that the president cut $716 million from Medicare to help pay for the Affordable Care Act. 
 
 Romney was eager to launch into a critique of the landmark legislation that he cited as his top example of programs that must be eliminated to close the federal deficit. “I apologize, Mr. President,” Romney added after referring to the program as Obamacare. “I use that term with respect.” 
 
 “I like it,” Obama quickly responded, but that was about their only real point of agreement. 
 
 Romney argued that the program would raise health-care costs and make it less likely that businesses would hire new workers. He accused Obama of establishing an unelected board to make health-care decisions for patients, and of cutting more than $700 billion from Medicare to help pay for the law. And he chastised the incumbent for “pushing through” legislation of such magnitude without a single Republican vote. 
 
 “I just don’t know how the president could have come into office — facing 23 million people out of work, rising unemployment, an economic crisis at the kitchen table — and spend his energy and passion for two years fighting for Obamacare instead of fighting for jobs for the American people,” Romney said. “It has killed jobs.” 
 
 Obama pushed back, particularly on the point about the cut to Medicare, which he explained, and independent analysis has shown, does not include direct reductions to benefits for seniors but rather ratchets down payments to providers, including insurance companies. 
 
 The president noted that Romney has promised to repeal Obamacare on his first day in office, yet more recently has said he wants to keep some of its provisions, notably its protections for patients with preexisting conditions and the rights of young adults to remain on their parents’ insurance plans. 
 
 Obama also reminded viewers that his law was modeled heavily on the health-care law that Romney championed when he was governor of Massachusetts. “We’ve seen this model work really well in Massachusetts,” the president said. 
 
 “He now says he’s going to replace Obamacare and ensure that all the good things that are in it are going to be in there and you don’t have to worry,” Obama added. “And at some point, I think the American people have to ask themselves: Is the reason that Governor Romney is keeping all these plans to replace secret because they’re too good?” 
 
 Romney defended his plan in Massachusetts, saying he had not raised taxes and had pushed through the bill with significant numbers of Democratic votes. 
 
 On energy, Obama said Romney would continue to favor tax breaks for the oil industry. Romney retorted by noting that the Obama administration has invested more than $90 billion in green-energy projects, “about about 50 years’ worth of what oil and gas receives.” 
 
 On regulatory issues, Romney attacked the Dodd-Frank Wall Street Reform and Consumer Protection Act, which overhauled regulation of the financial industry, but he said that some regulations are needed and that he would keep them. Obama scoffed at Romney’s promise to repeal Wall Street regulation that he signed into law, saying: “Does anybody out there think that the big problem we had is that there was too much oversight and regulation of Wall Street? Because if you do, then Governor Romney is your candidate.” 
 
 Near the end of the debate, Lehrer asked the candidates how they might make Washington work more effectively. Romney said he would do what he had done with a Democratic legislature in Massachusetts: work out compromises. 
 
 Obama said that might be difficult if one of Romney’s first efforts were to repeal the Affordable Care Act, which he said would anger Democrats in Congress. And he accused Romney of being hostage to the most conservative elements of the Republican Party. 
 
 “I’ve got to tell you, Governor Romney, when it comes to his own party during the course of this campaign, has not displayed that willingness to say no to some of the more extreme parts of his party,” he said. 
 
 David Nakamura and Philip Rucker contributed to this report.
– Facts and numbers were flying in last night's debate, and President Obama and Mitt Romney agreed on so few of them that "the two men seemed to be inhabiting two parallel universes," Politico observes. Thankfully, a swarm of fact-checkers have been poring over the candidates' statements to sort things out. Here are some of the more egregious fibs: Romney: "I won't put in place a tax cut that adds to the deficit." Independent analysis indicates that Romney's tax plan would add $5 trillion to the deficit over 10 years. Romney says he'll pay for that by reducing deductions and credits, but the Tax Policy Center concluded that was "mathematically impossible." Obama: "We've made some adjustments" to Simpson-Bowles. Obama's plan is not, as he implied, comparable to Simpson-Bowles. It's much less aggressive, doesn't touch Social Security, and, while it too reduces the deficit by $4 trillion, it takes an extra year to do it. Romney on green energy loan recipients: "I think about half have gone out of business." Try three out of 26. Romney: Dodd-Frank "designates a number of banks as too big to fail." The law designates some banks for special treatment, but that treatment involves extra regulation and a way to liquidate them if they run into trouble; they are not, as Romney argued "effectively guaranteed by the federal government." Romney: "Pre-existing conditions are covered under my plan." Romney's health care plan only covers people with pre-existing conditions if they "maintain continuous coverage," which was more or less the situation before ObamaCare. Obama: "Under Governor Romney's definition … Donald Trump is a small business." Romney's plan doesn't actually define small businesses. But the federal government does, and under its guidelines, Trump is a small business, because he owns some businesses with fewer than 500 employees, according to CNN. Obama: "I've put forward a specific $4 trillion deficit reduction plan." True, but that plan counts savings already agreed on during the debt ceiling debate. Romney: "The president said he'd cut the deficit in half. Unfortunately, he doubled it." When Obama took office, the projected deficit for 2009 was $1.2 trillion. For fiscal 2012, the deficit is expected to be $1.1 trillion, the New York Times reports.