Obama met with top Democrats at the White House and spoke by phone with Senate Republican leader Mitch McConnell.
"He needs to indicate what he will sign, and we are in those discussions," McConnell said of the president. He added he had also spoken with Vice President Joe Biden, who played a prominent role in earlier attempts to break the gridlock that has pushed the country to the verge of an unprecedented default.
"We have until midnight," said Reid before leaving for the White House.
Obama is seeking legislation to raise the government's $14.3 trillion debt limit by enough to tide the Treasury over until after the 2012 elections. He has threatened to veto any legislation that would allow a recurrence of the current crisis before early 2012 but has agreed to Republican demands that deficits be cut - without tax increases - in exchange for additional U.S. borrowing authority.
At a news conference in the Capitol, Speaker John Boehner said that despite the partisanship of recent weeks, "I think we're dealing with reasonable, responsible people who want this crisis to end as quickly as possible and I'm confident it will."
Without a compromise in place by next Tuesday, administration officials say the Treasury will run out of funds to pay all the nation's bills. They say a subsequent default could prove catastrophic for the U.S. economy and send shockwaves around the world. With financial markets closed for the weekend, lawmakers had a little breathing room, but not much. Asian markets begin opening for the new work week when it is late Sunday afternoon in the capital.
The sudden talk of compromise contrasted sharply with earlier developments as both the House and Senate convened for unusual Saturday sessions.
The House voted down legislation drafted by Democrat Reid to raise the government's debt limit by $2.4 trillion and cut spending by the same amount.
The vote was 246-173, mostly along party lines and after debate filled with harsh, partisan remarks .
Within minutes, White House officials disclosed the meeting with Reid and Pelosi.
Before the House vote, Republicans said the Reid spending-cuts plan was filled with gimmicks and would make unacceptable reductions in Pentagon accounts. "It offers no real solutions to the out-of-control spending problems," said Rep. Alan Nunnelee of Mississippi, part of a group of 87 first-term Republicans who have led the push for deeper spending cuts.
Not even Democrats seemed to like the legislation very much, although many emerged from a closed-door meeting of the rank and file saying they would vote for it.
Rep. Lloyd Doggett, D-Texas, called it "the least worst alternative to avoid default."
Yet with their votes, many Democrats signaled their readiness for compromise by voting to cut spending without raising taxes. Many Republicans insist taxes must not be raised to cut into federal deficits, even for the wealthiest Americans and for big oil companies.
In remarks on the House floor, Rep. David Dreier, R-Calif., said the vote itself could be prelude to a final effort at compromise that would involve the White House and the leaders of both parties.
Across the Capitol, the Senate marked the hours before a scheduled test vote at 1 a.m. Sunday on the same measure.
There was no doubt about the outcome there, either, unless compromise intervened.
A total of 43 Republicans sent Reid a letter saying they would block the bill from advancing, enough to prevail.
With both parties' preferred solutions blocked, the only alternatives were compromise that was so far elusive or a default that no one claimed to want.
The day's events in the House were orchestrated as political payback, and unusual at that, since Republicans lined up to kill legislation that hadn't even cleared the Senate.
Less than 24 hours earlier, Reid had engineered the demise of a House-passed bill hours after it passed, and without so much as a debate on its merit.
Saturday's proceedings in the House were particularly partisan.
Pelosi said Boehner "chose to go to the dark side" when he changed his own legislation to satisfy tea party lawmakers and other critics.
There were catcalls from the Republican side of the aisle at that, and Pelosi responded by repeating that the speaker "chose to go to the dark side."
Republicans ridiculed Reid's legislation.
"Not only does it fail to address our spending and debt problem, it won't even prevent a downgrade of our credit rating," said Rep. Scott Garrett, R-N.J. "We need actual cuts to government spending to address our long-term debt crisis, not phantom cuts and accounting gimmicks."
Only 24 hours earlier, the House measure squeaked through on a 218-210 vote, with 22 Republicans joining united Democrats in opposing the GOP bill. It paired an immediate $900 billion increase in U.S. borrowing authority with $917 billion in spending cuts spread over the coming decade.
While Republicans said it marked the second time the House passed legislation to raise the debt limit - compared to none for the Senate - they also acknowledged Boehner's leverage had been diluted.
He had hoped to pass the bill on Thursday but was forced into a postponement because of objections from tea party-backed conservatives and other critics.
To win their votes, he was forced to add a provision that would require Congress to approve a constitutional balanced budget amendment as a condition for an additional debt limit increase after the initial $900 billion installment.
In addition to driving away some of Boehner's own Republicans, that inflamed Democrats, who seized on it as a surrender to parts of his rank and file who refuse to compromise.
Associated Press writers Donna Cassata and Matt Yancey contributed to this story.