“I’ve been left at the altar now a couple of times,” Mr. Obama said. “And I think that one of the questions that the Republican Party is going to have to ask itself is, Can they say yes to anything?”

This time, however, Mr. Obama had also faced a firestorm from within his party, because of the spending cuts he was considering with Mr. Boehner.

Hours before the tempest, the three top stewards of the nation’s financial system — Treasury Secretary Timothy F. Geithner; Ben S. Bernanke, chairman of the Federal Reserve, and William C. Dudley, president of the Federal Reserve Bank of New York — had met to discuss how to react to shield the economy from the blow if Congress failed to raise the debt limit. But in a joint statement, they said they remained confident Congress would act.

Mr. Obama, too, said he thought that default could be avoided. “I am less confident at this point that people are willing to step up to the plate and actually deal with the underlying problem of debt and deficits,” he said at his news conference.

Mr. Boehner said he would work now with Senate leaders on a plan to raise the debt limit.

Just what form the new legislative proposal will take was uncertain, as lawmakers and their top aides had only opened talks about how to proceed. Some expected it to be built upon an earlier plan by Senator Mitch McConnell of Kentucky, the Republican leader, who employed an arcane process to allow a debt limit increase to occur over the objections of Congress.

But in a statement, Mr. McConnell noted that the speaker had expressed an interest in trying to find a “new path forward” with Senate Democrats, suggesting that he wanted to go in a different direction than the McConnell plan, which had drawn stiff opposition in the House. It could still provide a last-ditch alternative if all else fails.