Washington ( CNN ) -- They are losing the battle over higher taxes on the wealthy , so now Republicans are threatening a political war next year when it comes time to raise the nation 's debt ceiling . With cracks appearing in their anti-tax facade and polls showing most Americans favoring President Barack Obama 's stance in the fiscal cliff negotiations , GOP legislators are starting to advocate a tactical retreat to fight another day . Conservative Sen. Lindsey Graham , R-South Carolina , promised the newly re-elected Obama `` one hell of a fight '' next year if the president forces through his plan for high-income earners to pay more taxes without agreeing to substantive steps to reduce the nation 's chronic federal deficits and debt . `` But there will come a time in February and March where we have to raise the debt ceiling , '' Graham said Tuesday on `` Piers Morgan Tonight '' on CNN . `` I will not raise the debt ceiling ever again until we get significant entitlement reforms , because if we do n't reform entitlements , we 're going to become Greece , '' adding that the situation presented a chance for Obama to lead . `` But if he does n't lead , there 's going to be one hell of a fight over raising the debt ceiling . '' Survey : 70 % want compromise . Senate Republican leader Mitch McConnell concurred on Tuesday , telling reporters that `` we are going to insist that we have another discussion about the future of our country in connection with his request of us to raise the debt ceiling . '' Meanwhile , McConnell and House Speaker John Boehner on Tuesday called for Obama to make public the specific spending cuts he will offer in a deficit-reduction deal . Both complained that Obama was deliberately holding up progress in negotiations by refusing to provide the details of his cost saving plans . `` Where are the president 's spending cuts ? '' asked Boehner , R-Ohio , the lead GOP negotiator . `` The longer the White House slow walks this process , the closer our economy gets to the fiscal cliff . '' In response , White House spokesman Jay Carney said Boehner and McConnell were wrong because Obama detailed his proposed spending cuts more than a year ago . He added that Republican negotiators had yet to offer any details of their own on how to raise more revenue from taxes , `` and it would be helpful if they did . '' House Democratic leader Nancy Pelosi , meanwhile , argued that the $ 1 trillion in spending cuts agreed to by Congress in the past two years should be counted toward deficit reduction in the current negotiations . `` Where are the cuts ? They 're in bills that you , Mr. Speaker , have voted for , '' Pelosi , D-California , said Tuesday . Three weeks remain to cut a deal before the automatic tax increases and spending cuts of the fiscal cliff go into effect on January 1 . Without an agreement during the current lame-duck session of Congress , everyone 's taxes will go up , and economists warn the impact of the fiscal cliff could cause another recession . Obama , Boehner speak by telephone after GOP counter-offer . However , the administration has signaled it can delay some of the effects to allow time to work out an agreement when a new Congress convenes in January . Obama has held a campaign-style series of public events to back his call for extending Bush-era tax cuts for 98 % of Americans while allowing rates to return to higher 1990s levels on income over $ 250,000 . The issue was central to his re-election in November , and Obama made clear on Monday that he intended to adhere to his belief that the wealthy must contribute more . `` I 'm willing to compromise a little bit , '' Obama said at a Michigan diesel engine plant . However , he said higher tax rates on the the top income brackets was `` a principle I 'm not going to compromise on . '' The president 's public push appears to be working as polls show that most Americans back the president 's position . A new Politico/George Washington University survey on Monday said 60 % of respondents supported Obama 's proposal compared with 38 % who opposed it . On Tuesday , a Gallup poll showed that 70 % of adult Americans want Congress and the White House to reach a compromise that would avoid the fiscal cliff . A similar Gallup poll last week said 62 % wanted compromise . The deficit-reduction debate hinges on the tax issue , with Republicans opposing any increase in tax rates in their quest to shrink government , while Obama and Democrats want to secure more tax revenue as part of a broader package . Americans already making big decisions over fiscal cliff . Both sides call for eliminating tax deductions and loopholes to raise more revenue , but Obama also demands an end to the tax cuts of 2001 and 2003 for the top brackets . Republicans oppose the return to higher rates , saying it will inhibit job growth because small business owners declare their profits as personal income and therefore would face a tax increase . In response , Obama and Democrats note that their plan -- already approved by the Senate and needing House approval to be signed into law by the president -- affects just 2 % of taxpayers and 3 % of small business owners . While Republicans argue those small business owners account for about half of all business income , Democrats say that 's because they include law firms , hedge funds traders and other high-income operations . Obama and Boehner met face to face on Sunday for the first time since November 16 . It also was their first one-on-one meeting in more than a year , when deficit talks broke down . The outline for a deal has become clear in recent weeks . Both sides agree that more revenue from taxes should be part of the equation , with Obama seeking $ 1.6 trillion and Republicans offering $ 800 billion . A source close to the talks said Tuesday that the White House had floated the idea of dropping the revenue target to $ 1.2 trillion , then went up to $ 1.4 trillion on Monday . Later , Boehner spokesman Michael Steel said his side made a counteroffer to the White House `` that would achieve tax and entitlement reform to solve our looming debt crisis and create more American jobs . '' Steel also said Boehner and Obama spoke on the phone after the Republican proposal was floated . Steel provided no further details on the counteroffer or the phone conversation , and repeated Boehner 's earlier assertion that Republicans were waiting for Obama to identify specific spending cuts he would be willing to make . Federal Reserve may buy more bonds . Boehner 's side wants additional revenue to come from tax reform , such as eliminating some deductions and loopholes , while Obama demands the higher rates on income over $ 250,000 for families as part of the equation . Republicans also seek savings from entitlement programs totaling another $ 800 billion or so , while Obama has proposed $ 400 billion in reduced entitlement costs . Social Security would not be included in the president 's plan . Another sticky issue -- whether the need to raise the federal debt ceiling early next year should be part of the discussion -- also remains unresolved . Obama says absolutely not , while Boehner says that any increase in government borrowing to pay its bills must be offset by spending cuts . Graham 's comments this week showed that Republicans plan to regroup around negotiations to raise the debt ceiling . From my home to the house : How to fix the fiscal cliff . He noted that Obama proposed making permanent a process originated by McConnell that would allow the president to increase the debt ceiling and Congress to then try to block it , an unlikely scenario given Democratic control of the Senate . `` That 's going nowhere , '' Graham told Fox News on Monday , adding : `` He 's not king . He 's president . '' However , a top House Democrat said that exploiting the debt ceiling for political gain would backfire on Republicans . `` Threatening to tank the entire economy , which is what would happen if we ever defaulted on our debt , is not a kind of negotiating strategy that is going to be popular with the American people , '' Rep. Chris Van Hollen told MSNBC on Monday . It remains unclear if a deal will happen before the end of the year or if the negotiations will carry over into 2013 , after the fiscal cliff takes effect . Without action now on the fiscal cliff , the nonpartisan Tax Policy Center estimates that middle-class families would pay about $ 2,000 a year more in taxes . Even with a deal , revisions in the tax code and other changes would mean everyone pays a bit more starting next year . All signs point toward a two-step approach sought by Obama , with initial agreement now on some version of his tax plan with targets set for comprehensive negotiations on a broader deficit reduction deal in the new Congress next year . Opinion : Generals , get real and cut Pentagon spending . Such an outcome would put off the main worry of the fiscal cliff , the expiration of the Bush-era tax cuts that would result in higher rates for everyone . Obama and Democrats say they would then be ready to negotiate significant savings from entitlement programs , while Republicans say they need to first see commitment on entitlement reforms before accepting any higher tax rates . McConnell , R-Kentucky , warned on the Senate floor on Tuesday that `` until the president gets specific about cuts , nobody should trust Democrats to put a dime in new revenue toward real deficit reduction or to stop their shakedown of the taxpayers at the top 2 % . '' He and Boehner want Obama to take some of the political heat for proposing cuts to entitlement programs and other government spending . On Tuesday , congressional Democrats rejected any cuts to the Medicaid health care system for poor and disabled Americans as part of a fiscal cliff deal . The opposition by Democrats showed the pressure Obama faces from his liberal base to avoid significant changes to the entitlement program that benefits millions . Some in Congress warn that the legislative process will need at least a week to work through potentially complex measures from any proposed deal , meaning there is a de facto deadline of Christmas Day at the very latest for negotiators . Retiring Sen. Kent Conrad , D-North Dakota , predicted Tuesday on MSNBC that a deal would get worked out in a week 's time . `` It would be wise on their part not to come too quickly with a deal because that would give all the interest groups a chance to get organized and try to kill it , '' Conrad said . `` And we know that on the right , on the left , special interest groups are just salivating at the chance to attack any agreement because , look , any agreement is going to have controversy attached to it . '' iReport : How will the fiscal cliff affect you ? CNN 's Dana Bash , Deirdre Walsh , Ashley Killough and Kevin Liptak contributed to this report .
NEW : White House , Republicans exchange counteroffers ; Boehner , Obama talks on phone . NEW : Obama promises ` ` one hell of a deal '' over debt - hike unless Congress cut . The White House battles GOP leaders over who wants specifics . Polls show most Americans back the president on raising taxes on the rich .