There were no immediate signs of a breakthrough, however. The lawmakers and Obama were unsmiling as the meeting began, and most of them avoided reporters when they left the White House.
In a statement released afterward, the White House said, "Congress should refrain from playing reckless political games with our economy. Instead, it should be responsible and do its job, avoiding default and cutting the deficit." The statement renewed Obama's insistence that any agreement tide the government over until after the 2012 elections, to avoid a rerun of the debt dispute in the heat of the campaign.
Senate Republican leader Mitch McConnell issued a somewhat more upbeat statement of his own.
"The president wanted to know that there was a plan for preventing national default," he said. "The bipartisan leadership in Congress is committed to working on new legislation that will prevent default while substantially reducing Washington spending."
House Speaker John Boehner also pledged to work for a bipartisan solution.
"As I said last night, over this weekend Congress will forge a responsible path forward," he said in a statement. "House and Senate leaders will be working to find a bipartisan solution to significantly reduce Washington spending and preserve the full faith and credit of the United States."
The meeting followed a collapse in negotiations late Friday, when Boehner announced he was breaking off talks with the president. A visibly irritated Obama summoned Boehner and three other top congressional leaders from both parties to convene Saturday and try again to find a way to raise the debt limit before an Aug. 2 deadline cuts off the government's borrowing authority.
The president was flanked at the bargaining table by Boehner and Democratic Senate Majority Leader Harry Reid of Nevada. Also at the table were Vice President Joe Biden, House Minority Leader Nancy Pelosi, D-Calif., and McConnell, R-Ky.
The president devoted his weekly radio and Internet address Saturday to the impasse and urged Republicans to make a deal.
"We can come together for the good of the country and reach a compromise. We can strengthen our economy and leave for our children a more secure future," the president said. "Or we can issue insults and demands and ultimatums at each another, withdraw to our partisan corners and achieve nothing."
Rep. Jeb Hensarling of Texas said in his party's weekly address that the Democrats were to blame.
"If we're going to avoid any type of default and downgrade - if we're going to resume job creation in America - the president and his allies need to listen to the people and work with Republicans to cut up the credit cards once and for all," he said.
Boehner and McConnell also criticized Obama and the Democrats before the Saturday meeting began.
"If the White House won't get serious, we will," Boehner's office said. A statement from the office noted that Obama has said he wants an agreement that will take care of the problem through the November 2012 elections.
"It would be terribly unfortunate if the president was willing to veto a debt limit increase simply because its timing would not be ideal for his re-election campaign," according to Boehner's office.
The Democratic Congressional Campaign Committee used the troubled talks to raise money with online appeals. An email from the group said that "after hard negotiating for two weeks" Boehner and other top GOP officials "irresponsibly just walked out of the room and quit talks with the White House."
The group said it was "launching a hard-hitting advertising campaign starting this weekend and continuing through August to hold Republicans accountable," but it gave no details.
At a news conference Friday after Boehner said he was withdrawing, Obama told reporters, "We have run out of time and they are going to have to explain to me how it is that we are going to avoid default.
Boehner accepted the invitation for Saturday's meeting even while arguing that Obama bore the blame for the collapse.
The political theater played out even as the deadline neared. Barring action by then, the Treasury will be unable to pay its bills. That could cause interest rates to rise, threaten the U.S. economic recovery and send shock waves around the globe.
The deadline pressure hasn't seemed to bring the parties closer, even though they all insist they do not want a default.
For the first time since talks began, Obama declined to offer assurances that a default would be avoided, although moments later he said he was confident of that outcome.
Obama said Boehner left a deal on the table that was better for Republicans than for Democrats, with $2.6 trillion in cuts outweighing new tax revenue of $1.2 trillion. The president said he was losing confidence that the underlying deficit problems would be dealt with even if the borrowing limit rose.
"I've been left at the altar now a couple of times," Obama said.
Still, aides on both sides said there was agreement on gradually raising the age of eligibility of Medicare from 65 to 67 for future beneficiaries, and slowing the increase in cost-of-living raises in Social Security checks.
Republican aides said Obama had upped his demand for higher taxes during the week. The aides said administration officials had tacitly agreed to $800 billion in new revenue over 10 years but that the White House backed away and wanted $400 billion more.
Aides said the two sides were not able to bridge their differences over the triggers designed to force Congress to enact both tax changes and cuts to Medicare and other benefit programs by early next year. Both sides also were apart on the size of cuts for Medicaid, the health care program for the poor and disabled.
Yet aides on both sides said the negotiations had yielded agreement for cuts of $250 billion from Medicare.
Associated Press writers Erica Werner, David Espo, Ben Feller and Jim Kuhnhenn contributed to this report.