?We are working, and I?m confident there will be resolution,? Mr. Boehner told fellow House Republicans on an afternoon conference call, according to participants. ?There has to be.?

Hours after that call, Mr. Boehner met in his Capitol office suite for about an hour with the other leaders of the House and Senate ? Senator Harry Reid, the majority leader; Senator Mitch McConnell, the Republican leader; and Representative Nancy Pelosi, the Democratic leader ? in an effort to iron out contentious points in an emerging deal they would like to make public on Sunday before the opening of financial markets in Asia.

President Obama opened a morning meeting with Congressional leaders at the White House by noting that global markets could react adversely to Friday?s collapse of his and Mr. Boehner?s negotiations as early as Sunday, when trading begins in Asia. His Treasury secretary, Timothy F. Geithner, reinforced the point at the meeting?s end.

The tense series of high-powered meetings on Saturday was reflective of the sense of urgency among lawmakers little more than a week before the federal government risks defaulting on its debts, a fate that could be avoided if Congress agrees to increase the $14.3 trillion debt ceiling. Congressional Republicans, Democrats and Mr. Obama have seized on the debt fight as a way to win approval of a debt-reduction package, but have disagreed sharply over what it should include.

The speaker, who abruptly broke off budget talks with Mr. Obama on Friday evening, said he hoped the plan could be finished within 24 hours and indicated on the conference call with House members that the savings would most likely be achieved in two stages.

As described by knowledgeable Congressional aides, the emerging agreement would enact a first round of cuts of just under $1 trillion, an amount they said was sufficient to clear the way for a debt limit increase through 2011. A second increase would follow after a newly created legislative commission considered a broader range of spending cuts, program overhauls and potential revenue increases.

But Republicans and Democrats were divided over how that second increase in the debt limit would be approved, since Democrats have dug in against anything they see as a short-term extension that would require multiple votes on the debt increase before the end of next year.

?I will not support any short-term agreement, and neither will President Obama nor Leader Pelosi,? Mr. Reid said in a written statement on Saturday. ?We seek an extension of the debt ceiling through at least the end of 2012. We will not send a message of uncertainty to the world.?

Mr. Reid and the other leaders met at the White House on Saturday morning at the request of Mr. Obama. The meeting broke up without resolution just before noon, after about an hour of discussion.

In a statement after the White House session, Mr. McConnell indicated that he and his leadership counterparts were trying to devise a fallback measure to assure the borrowing ceiling was raised in time.

?The president wanted to know that there was a plan for preventing national default. The bipartisan leadership in Congress is committed to working on new legislation that will prevent default while substantially reducing Washington spending,? Mr. McConnell said.

The White House, in its own statement, said that Mr. Obama reiterated his opposition to a short-term extension of the ceiling because it would hurt the economy, prompt rating agencies to downgrade the nation?s credit rating and drive up interest rates for all Americans.

?As the current situation makes clear, it would be irresponsible to put our country and economy at risk again in just a few short months with another battle over raising the debt ceiling,? the White House statement said.

The rancorous ending to the debt discussions on Friday means that leaders of the House and Senate now have only days to find a debt limit solution that has eluded them for months, gaming out ways to get a debt increase through a Republican-controlled House packed with conservatives demanding deep cuts and no new revenues.