But without a compromise in hand, the divided Senate could not break a filibuster and went wearily into recess while the leaders resumed their search for something that could pass.

Senator Harry Reid, the majority leader, had convened the Senate at noon, then moved to a procedural vote on his own proposal for raising the debt ceiling. Senate Republicans had been filibustering that plan, which House Republicans rejected on Saturday, and the vote on breaking the filibuster fell 10 votes short of the 60 votes needed under Senate rules. Even so, Mr. Reid said before the cloture vote that he was ?cautiously optimistic? that an agreement could be reached today that would make it possible for the Senate to amend his bill and gain bipartisan approval in both chambers.

But Mr. Reid said that ?there are a number of issues that must be resolved.?

?Our optimism in days past has been really stomped on,? he said.

Senator Mitch McConnell of Kentucky, the Republican leader, said Sunday that he was ?very close? to recommending to his members that they sign on to a debt deal with President Obama and the Democrats.

Speaking on the CNN program ?State of the Union,? Mr. McConnell said the emerging deal included as much as $3 trillion in cuts over the next 10 years, with much of that to be decided later this year by the joint Congressional committee. Senator Charles E. Schumer of New York, a top Democratic leader, also sounded optimistic in an appearance on the same news program, but he had some reservations.

?I feel a lot better today about the ability to avoid default than I did even yesterday morning,? he said. ?And default would have such disastrous consequences for our nation for decades to come,? he continued. ?The fact that our leaders are talking, though hardly anyone agrees with everything that?s come up, is a good thing.?

The first indication that the hard lines were softening came Saturday afternoon, when the two leading Congressional Republicans announced that they had reopened fiscal talks with the White House and expected their last-ditch drive to produce a compromise. Following the House?s sharp rejection of Mr. Reid?s proposal, Mr. McConnell said he and Speaker John A. Boehner were ?now fully engaged? in efforts with the White House to find a resolution that would tie an increase in the debt limit to spending cuts and other conditions.

?I?m confident and optimistic that we?re going to get an agreement in the very near future and resolve this crisis in the best interests of the American people,? said Mr. McConnell, who noted that he was personally talking to both Mr. Obama and Vice President Joseph R. Biden Jr., a favorite partner in past negotiations.

Mr. Boehner, who would have to steer a compromise through the House, said he based his confidence on the sense that ?we?re dealing with reasonable, responsible people who want this crisis to end as quickly as possible.?

A Democratic official with knowledge of the talks said that Mr. McConnell called Mr. Biden early Saturday afternoon, the first conversation between the two men since Wednesday. The official said they talked at least four more times on Saturday as they tried to work out an agreement.

The deal they were discussing, this person said, resembled the bill that Mr. Boehner pushed through the House the House on Friday more than it did the one that Mr. Reid had proposed.

It would immediately raise the debt ceiling by about $1 trillion, accompanied by a similar range of spending cuts, and set up a bipartisan committee that would work to find deeper reductions in the deficit in exchange for a second debt limit increase that would extend through the 2012 elections.