WASHINGTON — A special congressional supercommittee acknowledged failure Monday in efforts to cut the federal deficit by at least $1.2 trillion, and President Barack Obama warned that he would veto any attempt to undo a resulting round of across-the-board spending cuts.

Obama said the threat of those reductions should remain in place to maintain pressure on Congress to find a compromise. He said the only way the automatic spending cuts would not take place is if Congress gets back to work and agrees to a “balanced plan” to reduce the deficit by $1.2 trillion.

“There will be no easy off-ramps on this one,” Obama said.

While Congress is on break for the Thanksgiving holidays, many members, especially Republicans, turned their attention Monday to the looming Pentagon cuts. Some were already saying they would try to spare the massive cuts to military spending.

“We need to more appropriately allocate spending reductions,” Sen. Jeff Sessions of Alabama, the ranking Republican on the Senate Budget Committee, said. “Congress could alter the sequestration,” the term for the automatic cuts. “I am hoping for that.”

The supercommittee co-chairmen, Sen. Patty Murray, D-Wash., and Rep. Jeb Hensarling, R-Texas, said they were “deeply disappointed” and “Despite our inability to bridge the committee’s significant differences, we end this process united in our belief that the nation’s fiscal crisis must be addressed and that we cannot leave it for the next generation to solve.”

The joint statement was issued after the close of U.S. stock markets, which had plunged. Democrats had pushed for a joint public appearance by the co-chairmen, but even that proved elusive.

Sen. John Kerry, D-Mass., had floated a last-minute tax plan and met in his office with a fellow Democrat on the panel, Rep. Chris Van Hollen of Maryland, along with Republican Sens. Jon Kyl of Arizona and Rob Portman of Ohio. There was no breakthrough, however, and the supercommittee’s nearly three months of work ended quietly.

Sen. Max Baucus, D-Mont., said panel members were discussing a “new idea” Kerry floated. Baucus declined to give details. Baucus said, “Both sides are feeling angst, more angst, at the possibility of no agreement, so they are working harder and more creatively.”

Aides to committee members said the discussions had not narrowed the vast differences between the two parties over taxes and entitlements.

It is unclear if any of the triggered reductions will actually take effect, since next year’s presidential and congressional elections have the potential to alter the political landscape before they would.

Based on accounts by officials familiar with the panel’s talks, it appeared that weeks of private negotiations did nothing to alter a fundamental divide between the political parties.

Democrats said they would agree to significant savings from benefit programs like Medicare, Medicaid and Social Security only if Republicans would agree to a hefty dose of higher taxes, including cancellation of Bush-era cuts at upper-income brackets.

In contrast, the GOP side said spending, not revenue, was the cause of chronic budget deficits, and insisted that the tax cuts approved in the previous decade all be made permanent.

Kerry told CNN, “This is a matter of fundamental fairness. We are stuck on this insistence of making the Bush tax cuts for the wealthy permanent. I think the American people will judge that to be insane.”

Kyl blamed Democrats for insisting that taxes on more affluent Americans be increased.

“Our Democratic friends said we won’t cut one dollar more without raising taxes,” Kyl said. “That tells you a lot about the ethos in Washington. We went into the exercise to try to reduce federal government spending. What we get from the other side is, no, we won’t make more cuts unless you raise taxes.”

The panel’s failure marked the end of an extraordinary yearlong effort by divided government to grapple with deficits that lawmakers of both parties and economists of all persuasions agree are unsustainable.

In the next month, lawmakers face deadlines to deal with several pressing issues: extension of a payroll tax holiday, extension of jobless benefits for the long-term unemployed, a 27 percent cut in Medicare payments to doctors and relief from the alternative minimum tax.

Items on this list carry big price tags. When Congress addressed them last year, the Congressional Budget Office said the temporary reduction in the payroll taxes would cost more than $110 billion, while the temporary extension of jobless benefits cost $55 billion and the remedy for the alternative minimum tax cost more than $130 billion.

Shielding doctors from pending cuts in their Medicare fees would cost at least $20 billion to $30 billion.

Republicans in both houses said they would insist that Congress find ways to offset most of these costs. Otherwise, they said, the upshot of a year focused on deficit reduction could be an increase in the deficit.

The Associated Press, New York Times and Washington Post contributed to this article.