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 ||||| 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. ||||| Story highlights Obama says Trump is a small business under Romney plan 
 
 The government defines small business as having under 500 workers 
 
 President Barack Obama invoked Donald Trump's name during Wednesday's presidential debate, claiming that GOP presidential candidate Mitt Romney would consider the mogul's empire a small business. 
 
 "Under Governor Romney's definition, there are a whole bunch of millionaires and billionaires who are small businesses," President Obama said. "Donald Trump is a small business. Now, I know Donald Trump doesn't like to think of himself as small anything -- but that's how you define small businesses if you're getting business income." 
 
 The facts: 
 
 While there is no universally accepted definition of a small business, the federal government defines it as any business that employs fewer than 500 people. 
 
 The Trump Organization employs 22,000 people. But Trump also runs a number of other companies that employ fewer than 500, meaning that -- under the federal government's definition -- he qualifies as a small business. 
 
 According to the U.S. Small Business Administration, which uses the 500-worker maximum in its definition, such firms employ half of all private-sector workers and pay 44% of the total U.S. private payroll. In 2009, there were 27.5 million businesses in the nation, 99.7% of which were small firms. 
 
 Photos: Photos: The first presidential debate Photos: Photos: The first presidential debate The first presidential debate – President Barack Obama and Republican presidential candidate Mitt Romney finish their debate in Denver on Wednesday, October 3. View behind-the-scene photos of debate preparations. Hide Caption 1 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney stands with his wife, Ann, and family following the first presidential debate. Hide Caption 2 of 31 Photos: Photos: The first presidential debate The first presidential debate – President Obama kisses first lady Michelle Obama after the debate Wednesday. It took place on their 20th wedding anniversary. Hide Caption 3 of 31 Photos: Photos: The first presidential debate The first presidential debate – Jim Leher of PBS moderates the 90-minute debate on Wednesday. It was the candidates' first time debating face to face. Hide Caption 4 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama defended his record and challenged his rival's proposals. Hide Caption 5 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney was more aggressive Wednesday in criticizing Obama's vision. Hide Caption 6 of 31 Photos: Photos: The first presidential debate The first presidential debate – People watch the debate at Galapagos Art Space in Brooklyn, New York. Hide Caption 7 of 31 Photos: Photos: The first presidential debate The first presidential debate – The event was expected to draw the candidates' largest nationwide audience to date. Hide Caption 8 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney answers a question from the moderator. Hide Caption 9 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama argues his view. Both candidates said the other's proposals won't work. Hide Caption 10 of 31 Photos: Photos: The first presidential debate The first presidential debate – Michelle Obama listens to the debate. Hide Caption 11 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney said Obama has failed to bring down high unemployment and get the economy surging again. Hide Caption 12 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama reacts to Romney's remarks on Wednesday. Hide Caption 13 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama listens during the debate in Denver. Hide Caption 14 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney, who has been unable to catch the president in most polls to date, sought to generate enthusiasm for a change in the White House. Hide Caption 15 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney's shadow is projected beneath text from the Declaration of Independence at the University of Denver's Magness Arena. Hide Caption 16 of 31 Photos: Photos: The first presidential debate The first presidential debate – The first of three presidential debates focused on domestic issues: the economy, health care and the role of government. Hide Caption 17 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama and Mitt Romney clashed over the economy on Wednesday. Hide Caption 18 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney speaks during Wednesday night's debate. The candidate called for a new economic path. Hide Caption 19 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama called for "economic patriotism" and said Romney's plan of tax cuts for the rich failed before. Hide Caption 20 of 31 Photos: Photos: The first presidential debate The first presidential debate – Romney and Obama wave to the crowd at the start of the presidential debate. Hide Caption 21 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama greets Romney on Wednesday. Hide Caption 22 of 31 Photos: Photos: The first presidential debate The first presidential debate – The candidates meet on stage less than five weeks before Election Day. Hide Caption 23 of 31 Photos: Photos: The first presidential debate The first presidential debate – Obama and Romney shake hands Wednesday night. Hide Caption 24 of 31 Photos: Photos: The first presidential debate The first presidential debate – The presidential race has been dominated so far by negative advertising as both camps try to frame the election to their advantage. Hide Caption 25 of 31 Photos: Photos: The first presidential debate The first presidential debate – Leher takes the stage Wednesday. It's his 12th time moderating a presidential debate. Hide Caption 26 of 31 Photos: Photos: The first presidential debate The first presidential debate – Michelle Obama points to Lehrer before the start of the debate. Hide Caption 27 of 31 Photos: Photos: The first presidential debate The first presidential debate – Ann Romney and first lady Michelle Obama hug on Wednesday. Hide Caption 28 of 31 Photos: Photos: The first presidential debate The first presidential debate – The candidates wives were in attendance for the most highly anticipated campaign event to date. Hide Caption 29 of 31 Photos: Photos: The first presidential debate The first presidential debate – Michelle Obama sits with White House Senior Advisor Valerie Jarrett, right. Hide Caption 30 of 31 Photos: Photos: The first presidential debate The first presidential debate – Rapper Will.i.am, left, speaks with Jarrett before the debate on Wednesday. View behind-the-scenes photos of debate preparations. Hide Caption 31 of 31 
 
 JUST WATCHED Analyst: Election now 'a horse race' Replay More Videos ... MUST WATCH Analyst: Election now 'a horse race' 01:40 
 
 JUST WATCHED Best 'zingers' from debate night Replay More Videos ... MUST WATCH Best 'zingers' from debate night 01:50 
 
 IRS data on the highest-income people in the country underscores that small business does not necessarily mean small profits. Of the top 400 people — who got $19.8 billion in S corporation and partnership net income in 2009 — 237 count as small businesses. 
 
 An analysis by the Urban Institute-Brookings Tax Policy Center finds that extending tax cuts for people who make more than $250,000 per year ($200,000 for single filers) would disproportionately help the richest taxpayers: 82% of the cut would go to people with more than $1 million in adjusted gross income, who would get an average tax cut of $164,000 apiece. 
 
 Romney's plan does not single out small businesses for special treatment. His plan attempts to lower taxes on all businesses -- big or small. 
 
 Conclusion: While Romney's plan does not define who is or is not a small business, some of Donald Trump's companies would qualify as a small business because they have fewer than 500 employees.
– 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.