Much of the rhetoric to date over the fiscal cliff has been on taxes, but lawmakers on Wednesday finally began to zero in on what might be the most difficult piece of the budget puzzle: raising the debt ceiling.

Democrats insist publicly that the GOP should meet both their major demands: raise taxes on annual income of more than $250,000, and get Congress out of the business of affirmatively raising the debt limit.

From the White House’s perspective, the debt ceiling fight of the past summer showed that markets and voters have no patience for brinkmanship when it comes to the full faith and credit of the United States. But Republicans, led by Speaker John A. Boehner of Ohio, have long insisted that the debt limit vote is their strongest point of leverage. And they don’t seem close to relenting.

The Republican position became clearer Wednesday as the GOP seemed to sense that it was time to draw bright lines on the issue. Meanwhile, Democrats doubled down on their stance that continuing to allow lawmakers to use the debt limit as a political tool would create an untenable situation going forward.

“I have to just tell you that is a bad strategy for America. It is a bad strategy for our businesses. And it is not a game that I will play,” President Barack Obama told business leaders at the White House. He was referencing the GOP’s inclination to use a debt ceiling vote to extract spending cuts from Democrats.

“There’s no uncertainty like the prospect that the United States of America, the largest economy that holds the world’s reserve currency, potentially defaults on its debts; that we give up the basic notion that the United States stands behind its obligations,” Obama continued.

The conversation surrounding the debt ceiling had been mostly muted. Even sources on the Democratic side conceded weeks ago their members were more concerned about tax rates. But the effects on markets of a potential default — or at least the threat of it — makes the issue the sleeping giant of the fiscal cliff talks.

The U.S. government will hit the debt ceiling sometime around the end of 2012, but Treasury can take extraordinary measures to extend the government’s borrowing capacity until the first few months of 2013.

But rather than give more power over the debt limit to the president, GOP rank-and-file members Wednesday began to fall in line behind their leaders’ opposition to the White House’s desired changes to debt ceiling votes. The Obama administration pitched a procedure modeled after the one proposed by Senate Minority Leader Mitch McConnell, R-Ky., as part of the 2011 debt limit deal, known as the Budget Control Act. The procedure would allow Congress to disapprove of any debt limit increases, but the president could still veto those resolutions of disapproval. (See the graphic below that explains how the McConnell provision works.)

Boehner and McConnell rebuffed Treasury Secretary Timothy F. Geithner on Nov. 29 in separate meetings.

Tea party favorite Sen. Mike Lee, R-Utah, said Wednesday that permanently changing the debt limit procedure would be “a gross abdication of our constitutional authority.”

“It will pass over my dead, lifeless body,” Lee said.

Rep. Tim Scott, R-S.C., another conservative player, echoed Boehner when he indicated that the debt limit was the GOP’s strongest weapon in forcing further deficit reduction.

“I think we should use our leverage,” he said. “The only way for us to have a serious conversation about the debt ceiling is to deal with spending first.”

Meanwhile, Sen. Rob Portman, an Office of Management and Budget director in the George W. Bush administration, planned to send a letter to Obama on Wednesday urging him to reconsider the administration’s proposed permanent changes to the debt limit procedure.

In the letter, the Ohio Republican used Obama’s 2006 vote as a senator against raising the debt ceiling as an example of why such votes have power in overall budget debates.

“For Congress to surrender its control over the debt limit would be to permanently surrender what has long provided the best opportunity to enact bipartisan deficit reduction legislation,” Portman wrote. “We also believe that Congress’s power over borrowing, like the power of the purse, is firmly rooted in our constitutional tradition.”

With the uptick in GOP messaging, Democrats are more concerned than ever about repeating their mistakes from the last lame duck in 2010, when they underestimated the GOP resolve to demand spending cuts equal to the amount of the debt limit hike.

It seems unlikely Democrats would be willing to trade on tax rates to secure an extension of the debt ceiling. But in one scenario Republicans have floated, they could gain leverage over Democrats if the GOP were to suddenly relent in the fight over the top tax rates and pass a bill to extending middle-class tax rates.

Rep. Sander M. Levin, ranking member of the Ways and Means Committee, said it would be best to deal with all tax and spending measures as a package that includes a debt limit increase, but that he wants Congress to act first and foremost on extending the 2001 and 2003 tax rates for middle-income Americans.

Even if that is off the table, the Michigan Democrat said, Democrats would have other leverage points, including extensions of the payroll tax cut, unemployment insurance, the alternative minimum tax, and of course, the threat that a U.S. government default could be calamitous for the world economy.

Tax rates for middle-income taxpayers is “the vital first step, and then we go on from there, but clearly it would be preferable to handle the debt ceiling,” Levin said.

Daniel Newhauser, Steven T. Dennis and Ben Weyl contributed to this report.