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“During the next year, there will be [EnLeader] opportunities to ameliorate the effect of this across-the-board sequestration,” Sen. Jon Kyl, Arizona Republican and a debt-panel member, said on CNBC Monday. “Certainly, there will be efforts to find offsets or other ways to reduce spending so that those cuts in defense spending don’t occur.”

The president has said he would veto any legislation aimed at undoing sequestration unless Congress comes up with alternative cuts or tax increases.

“There will be no easy offramps on this one,” he said. “We need to keep the pressure up to compromise, not turn off the pressure.”

The supercommittee — a compromise resulting from summer’s hard-fought deal to raise the debt ceiling — officially has until Wednesday night to vote on a plan to lower federal budget deficits by $1.5 trillion over the next 10 years. But, because the bipartisan Congressional Budget Office by law must have an analysis of the proposal ready 48 hours beforehand, the real deadline for a deal was the end of Monday.

Sen. Jeff Sessions of Alabama, the senior Republican on the Senate Budget Committee, partially blamed the secretive nature of the supercommittee and other bipartisan debt-reduction panels, including the so-called “Gang of Six.”

“These secret meetings disengaged the congressional process and prevented the serious national and legislative debate we need from taking place,” Mr. Sessions said. “It also allowed Democrats — who still had no real budget plan — to continue avoiding accountability for the fiscal and economic consequences of their political agenda.”

In remarks at the White House, Mr. Obama, just back from a nine-day trip overseas, made no bones about placing blame squarely on one party.

“Many Democrats in Congress were willing to put politics aside and commit to reasonable adjustments,” the president said. “But despite the broad agreement that exists for such an approach, there are still too many Republicans in Congress who have refused to listen to the voices of reason.”

Mr. Obama has taken heat, though, for not getting involved in the negotiations, and for being away during the final days before the deadline.

On Monday, New York Mayor Michael R. Bloomberg, a political independent, used a news conference to say that the failure rests with the president.

“It’s the chief executive’s job to bring people together and to provide leadership. I don’t see that happening,” Mr. Bloomberg said.

He added, “The executive branch must do more than submit a plan to a committee — and then step aside and hope the committee members take action. That’s not how any CEO would run a business, and at least in modern times, it’s not how landmark pieces of legislation have gotten through Congress.”

With about a month left this year, Mr. Obama called for Congress to act on extending the payroll tax cut to which he and lawmakers last year, saying that middle-class families otherwise would face a $1,000 tax increase.

But the next big step could come in February, when Mr. Obama’s 2013 budget is due and he will have to lay out how the automatic cuts would be absorbed.