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 don't reform entitlements, we're going to become Greece," adding that the situation presented a chance for Obama to lead. "But if he doesn't lead, there's going to be one hell of a fight over raising the debt ceiling."
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.
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.
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.