Republican lawmakers—and specifically the Tea Party wing of the GOP—are being told by a growing number of conservatives to stop using the debt ceiling crisis to force major spending cuts.
Instead, they're being told to battle over the separate issue of sequestration.
Sequestration—the massive forced cuts in government spending that were delayed by the "fiscal cliff" deal— will happen automatically on March 1 unless Congress votes to change it. The fight over that issue promises to be just as bruising at the debt ceiling.
The debt ceiling, meanwhile, has to be raised by Congress sometime in the next two months from the current $16.394 trillion or the U.S. won't be able to pay its bills. (Read more: Debt Ceiling Battle: Why No One Agrees on Anything)
"It would be a grave mistake to use the debate on the debt ceiling to get President Obama to agree to spending cuts," Alan Simpson, co-founder of the Campaign to Fix the Debt and former GOP senator from Wyoming told CNBC's "Closing Bell" Tuesday.
"I know they're (GOP lawmakers) going to try it and how far they'll go with that game of chicken I have no idea," said Simpson, who was co-chair of the Simpson-Bowles Commission that looked at reducing government debt.
Other conservatives like former House Speaker Newt Gingrich have also warned against holding up the debt ceiling vote. So have the Chamber of Commerce and the Business Round Table— with each saying it would be bad politics and hurt the GOP's standing with the public.
And now, a group funded by the billionaire Koch Brothers—Charles and David—is calling for the GOP to pull back during debt ceiling talks.
"We're saying focus on overspending instead of long-term debt," Tim Phillips, president of Americans for Prosperity said in an interview. "We're going to have a hard line on the sequester cuts." (Read more: Koch Group Urges Restraint on Debt Talks)
President Obama has declared that he won't negotiate over the debt ceiling. He's said that raising the ceiling does not authorize any new spending but simply allows the government to continue to pay for obligations to which Congress has already agreed. Even Federal Reserve Chairman Ben Bernanke has backed that view.
Analysts say that allowing the U.S. to default on payments for items like Social Security, Medicaid and defense could lower the country's credit rating and send stock markets into a freefall.
The debt ceiling's been raised some 74 times since 1962. Ten of those times have occurred since 2001.
Republicans like Sen. Tom Coburn (R-Okla.) claimed that a Republican-led refusal to raise the debt ceiling could be a "wonderful experiment" in forcing the government not to spend money on "stupid things."
The Tea Party Patriots, the nation's largest tea party group, said the Obama administration "has spent four years driving up the deficit and stalling when it comes to spending cuts, forcing Republicans to take drastic action such as threatening to hold the line on raising the debt limit or shut down the government to get Democrats to negotiate on spending."
But major cuts are coming in March due to sequestration. Congress was unable to reach agreement on forced spending cuts in January that were part of the fiscal cliff deal. They were delayed until this March as part of the American Taxpayer Relief Act of 2012—the deal that avoided the full 'fiscal cliff.'
The delay was to give lawmakers more time to agree on which programs would actually receive cuts.
The deficit reduction sequester is designed to enforce savings of $1.2 trillion through 2021. It calls for roughly a $55 billion cut in defense and a $55 billion cut in non-defense spending.
Will the GOP listen to it's critics and vote to raise the debt ceiling? Timothy Nash, a professor in economics at Northwood University, believes they will and still remain a force on Capitol Hill.
"I think the Tea Party still has relevance if it sticks with the view of getting our fiscal house in order," said Nash. "Democrats and Republicans share the same belief about lowering the debt."
"The debt ceiling is a short term issue and will likely get done," Nash argued. "The real issue is long term debt and everything should be on the table when it comes to cuts. We can't keep kicking our economic can down the road."