With tensions high at a rare weekend session, the legislation failed on a 246-173 vote that was largely symbolic. The Senate has yet to vote on the bill.
Saturday's result, however, could pave the way for negotiations on a compromise with Tuesday's deadline on the government's ability to pay its bills fast approaching. Senate Democratic Leader Harry Reid, D-Nev., and House leader Nancy Pelosi, D-Calif., were heading to the White House late Saturday.
Obama, in his weekly radio and Internet address, warned that "there is very little time" and pleaded with both Republicans and Democrats to stop political gamesmanship.
"The time for compromise on behalf of the American people is now," Obama said.
Pelosi, for her part, told the House it was "time to end this theater of the absurd. It's time for us to get real."
Resolution remained elusive. Some 43 Senate Republicans said they opposed the Democratic bill by Reid. His alternative measure would raise the debt limit by $2.4 trillion while cutting spending by $2.2 trillion.
In a letter to Reid, they wrote that the bill "fails to address our current fiscal imbalance and lacks any serious effort to ensure that any subsequent spending cuts are enacted." The 43 are enough to block passage of Reid's bill.
Setting the stage for the high-stakes weekend, Senate Democrats late Friday killed a House-passed debt-limit increase and budget-cutting bill less than two hours after it squeaked through the House. Reid set up a test vote for the wee hours of Sunday morning to break a GOP filibuster on his own legislation.
Saturday's debate in the House was heated and sometimes nasty, with occasional efforts to shout down speakers. Rep. Sander Levin, D-Mich., railed against the "pernicious nonsense" from Republican Rep. David Dreier of California.
Freshman Rep. Alan Nunnelee, R-Miss., said, "This Harry Reid plan offers no real solutions to the out-of-control spending problems."
Countered Rep. Jim Clyburn, D-S.C.: "The clock is ticking and Republicans are continuing to play political games."
Rep. Jerry Lewis, R-Calif., read a statement that then-Sen. Barack Obama had delivered years ago against raising the debt limit.
House Democrats said they would put aside their resistance to legislation that makes deep spending cuts and back the measure in a show of strength that could improve Reid's leverage in negotiations.
"There are some misgivings, but it's the only game in town," said Rep. Gerald Connolly, D-Va., as he emerged from an hour-long closed door meeting.
Democrats, Republicans and the White House, meanwhile, were expected to be deep in conversation in hopes of a potential compromise. Senate GOP leader Mitch McConnell of Kentucky was likely to play a pivotal role.
The outcome of the weekend endgame was anything but clear as Democrats and Republicans remained at odds over how to force lawmakers to come up with additional budget savings later this year beyond the almost $1 trillion in agency budget cuts over the coming decade that they basically agree on.
At the start of the Senate's session Saturday, Reid appealed to Republicans to work with him on his proposal, particularly McConnell.
"We're willing to listen to Republican ideas to make this proposal better, but time is running short," Reid said.
McConnell said the Reid plan wasn't "going anywhere. Senate Republicans refuse to go along with this transparently political and deeply irresponsible ploy to give the president cover to make our debt crisis even worse than it already is."
After a brutal week on Wall Street — investors lost hundreds of billions of dollars as the markets lost ground every day — pressure is intense to produce an accord before the Asian markets open on Sunday afternoon.
The House measure squeaked through on a 218-210 vote, with 22 Republicans joining united Democrats in opposing the GOP measure, which pairs an immediate $900 billion increase in U.S. borrowing authority along with $917 billion in spending cuts spread over the coming decade.
Friday's roll call came after Boehner had been forced to call off a vote slated for Thursday in the face of tea party opposition to the measure. He added a provision requiring that a second, up to $1.6 trillion debt increase be conditioned on House and Senate passage of a balanced-budget amendment to the Constitution, which would require an unrealistic two-thirds vote by each chamber to send it to the states for ratification.
Boehner's move only cemented Democratic opposition to the measure and complicated prospects for a weekend compromise that could clear both houses and win Obama's signature by next Tuesday's deadline. And by appeasing the tea party by adding the balanced-budget amendment poison pill, Boehner seemed to hand endgame leverage to Reid and Obama.
Boehner said the House bill — before the addition of the balanced-budget amendment — mirrored an agreement worked out with Reid last weekend.
Still, as soon as the measure reached the Senate side of the Capitol, Senate Democrats scuttled it. The vote was 59-41, with all Democrats, two independents and six Republicans joining in opposition.
Reid's alternative measure would raise the debt limit by up to $2.4 trillion, enough to meet a demand by Obama that the increase be sufficient so that Congress doesn't have to wrestle with it again until 2013.
Administration officials say that without legislation in place by the end of Tuesday, the Treasury will no longer be able to pay all its bills. The result could inflict significant damage on the economy, they add, causing interest rates to rise and financial markets to sink.
Executives from the country's biggest banks met with U.S. Treasury officials to discuss how debt auctions will be handled if Congress fails to raise the borrowing limit before Tuesday's deadline.
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Associated Press writers Donna Cassata and David Espo contributed to this story.
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