Pessimism mounted among members of the committee about their ability to strike a deal by Monday and avert a high-profile failure that would demonstrate anew the inability of the two parties on Capitol Hill to reach consensus about how to attack the nation’s mounting public debt. The partisan divide was also showcased Friday by a vote in the House to reject a Republican-backed constitutional amendment requiring a balanced federal budget.

Despite time running out on the committee created by the summer agreement to raise the federal debt limit, negotiations were in disarray, with Republicans and Democrats even disputing what precisely divided them. One panel member said that he still had slim hope for a deal but that it would take an extraordinary development to end the stalemate and avoid a series of automatic cuts in 2013 that would reduce federal services and make substantial reductions in Pentagon spending.

Seeking to reach at least a partial accord, Republicans made their six Democratic counterparts on the committee an offer that would get to roughly half of its goal — a retreat for an earlier plan with cuts in spending and revenue increases — but Democrats rejected it out of hand as inadequate. Democrats said the proposal was unbalanced because it was overly dependent on spending cuts with only a small amount of new revenue.

“If they maintain this,” said Representative James E. Clyburn of South Carolina, a Democratic member of the committee, in an interview, “then this is not going to happen.” Mr. Boehner, stepping in to the talks as the deadline neared, helped devise the Republican proposal, which offered less in new revenues than a previous Republican plan. But Republicans said the proposal also would not touch Medicare, Medicaid or Social Security, so they said they were surprised it was spurned. Mr. Boehner left town on Friday pessimistic that a deal could be made by the Monday evening deadline, his aides said.

“This was a balanced, bipartisan plan,” said Kevin Smith, a spokesman for Mr. Boehner. “The fact that it was rejected makes it clear that Washington Democrats won’t cut a dime in government spending without job-killing tax hikes.”

Senator John Kerry, Democrat of Massachusetts and a member of the committee, said in an interview that he still had hope, but that “we’re really having a hard time bringing our colleagues to what is fair, what is balanced.”

Aides to lawmakers in both parties, speaking anonymously because they did not want to be seen as sabotaging the negotiations, were even more negative. “I do not feel any last-minute sense of urgency,” one said.

The group has until Monday to submit a plan to the Congressional Budget Office for evaluation before presenting it to the full Congress on Wednesday, leaving time for reaching the sort of last-minute breakthrough that often occurs on Capitol Hill when lawmakers face a deadline. But members said the divisions were so deep, and good will so lacking, that their expectations were eroding.

The divide was further illustrated by the House’s rejection of a constitutional amendment that would generally require the federal government to balance its budget. The House voted 261 to 165 in favor of the proposal, but that was 23 votes short of the two-thirds majority needed to advance a constitutional amendment. The vast majority of Republicans supported the measure. Democrats, even some who voted in favor of a similar measure in 1995, pushed it to failure.

The dynamic Friday mirrored that of other high-stakes fiscal fights in the 112th Congress, like the brawl last summer over legislation to lift the debt ceiling and avoid default and a fight over a spending measure that was also resolved within hours of a government shutdown. But without an immediate threat of fiscal calamity, as was the case in both those instances, the cuts to federal spending triggered by a committee failure would not take place until 2013, leaving Congress an opportunity to find other escape hatches.

Republicans and Democrats provided radically different descriptions of the Republicans’ latest offer, intended to reduce budget deficits by $643 billion over 10 years. Republicans said their proposal called for $229 billion in new revenue and fees, including taxes on owners of corporate jets, and $316 billion in cuts in spending, including $100 billion from the Defense Department. Republicans said these cuts would reduce the need for federal borrowing and thus reduce interest payments on the federal debt by $100 billion over 10 years.

Democrats said the amount of tax revenue in the Republicans’ plan — $3 billion from owners of corporate jets — was laughable.

Central to the impasse is a fundamental disagreement over how much revenue would be raised toward the $1.2 trillion, and what the role of the Bush-era tax cuts, which are set to expire at the end of next year, would play. Republicans want to maintain the cuts; Democrats want them eliminated for the nation’s highest earners.

Most members of the committee intend to stay in town over the weekend and continue talking. Half the members are scheduled to appear on the Sunday morning television talk shows, where they will almost certainly have to discuss whether their efforts are doomed. Members of the panel are trying to figure out how to manage the denouement of the panel’s narrative, which began with their first meeting 10 weeks ago.

One option is for the panel to meet and vote next week on deficit reduction plans devised by the two parties. However, Congressional leaders are cool to that idea, saying it makes no sense to have the public embarrassment of a meeting that would showcase a failure to solve some of the nation’s biggest problems.

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