With the tax portion of the fiscal cliff cleared, Republicans are gearing up for a big battle over the debt ceiling, hoping to secure new spending cuts.

But President Barack Obama, who negotiated with Speaker John A. Boehner in 2011 over raising the debt ceiling, is solemnly promising not to repeat the process now that a new increase is needed.

“I will not negotiate around the debt ceiling. We’re not going to play the same game that we saw happen in 2011 — which was hugely destructive; hurt our economy; provided more uncertainty to the business community than anything else that happened,” Obama said at a Dec. 19 press conference.

That prompts questions, such as: Do Democrats really think Republicans will cave, leaving their demands for spending cuts aside? Or are they ready to hit the debt ceiling and blame the resulting economic consequences on the GOP?

In a closed-door meeting with House Democrats Tuesday, Vice President Joseph R. Biden Jr. swore that Obama would not budge on the debt ceiling, and that Republicans would cave.

Biden said the business community would urge Republicans to give in, and specified that the Wall Street Journal editorial board would be an especially influential source of pressure on the GOP.

Many Democrats, even some who entered the meeting with doubts, left the encounter believing that Obama was truly serious about not budging on the matter.

But others had doubts.

Rep. Peter A. DeFazio, D-Ore., said the agreement on extending the Bush-era tax rates for income under $450,000 left Democrats without “any leverage” in the debt ceiling fight.

DeFazio had harsh criticism for a statement by the White House recently saying Obama would not move to unilaterally overcome the debt ceiling under his authority in the 14th Amendment to the Constitution, which some argue grants the president that power.

“He already gave away the 14th Amendment, didn’t he? So how’s he gonna stand firm?” DeFazio said. “I don’t think they’re assessing the tea party caucus of the Republican Party, which really drives things here. They’re saying ‘one Wall Street Journal editorial and they’ll cave.’ Not any more. That’s the old Republicans.”

Rep. Elijah E. Cummings, D-Md., said Biden provided Democrats a “game plan” for how Democrats will deal with the debt ceiling.

The plan? According to Rep. Gene Green, D-Texas, Biden said the automatic spending cuts in the “sequester,” which are feared by many Republicans because of their impact on the Pentagon, could form leverage for Obama.

“We still have the sequestration to negotiate, and that’ll be at the same time that we have the debt ceiling issue. So we kicked the can down the road for a couple months, so at the same time we’ll be dealing with that,” Green said.

In a speech New Year’s Eve at the height of Senate talks over the fiscal cliff, Obama introduced a new demand for negotiations over replacing the automatic cuts in the sequester agreed to in the 2011 debt deal.

Obama said any replacements for the cuts should comprise a “balance” of other cuts and tax increases.

“I want to make clear that any agreement we have to deal with these automatic spending cuts that are being threatened for next month, those also have to be balanced — because remember, my principle has always been let’s do things in a balanced, responsible way. And that means that revenues have to be part of the equation in turning off the sequester, in eliminating these automatic spending cuts, as well as spending cuts,” Obama said.

But for all the promises of taking a hard line, Republicans in the House are just as adamant they will not budge on their demands over the debt ceiling.

Republicans said the terms of the tax deal they passed Tuesday, which they hate and mostly voted against, mean it is more important to hold strong on the debt ceiling increase.

“That’s Custer’s last stand, right there. But, we will have taken taxes off the table,” said Rep. John Fleming, R-La.