WASHINGTON -- Negotiations over a last-ditch agreement to head off large tax increases and sweeping spending cuts in the new year appeared to resume on Sunday afternoon after Republican senators withdrew a demand that any deal must include a new way of calculating inflation that would lower payments to beneficiary programs like Social Security and slow their growth.
Senate Republicans emerged from a closed-door meeting to say they agreed with Democrats that the request -- which had temporarily brought talks to a standstill -- was not appropriate for a quick deal to avert the tax increases and spending cuts starting Jan. 1.
To hold the line against raising taxes on high-income households while fighting for cuts to Social Security was "not a winning hand," said Senator John McCain, Republican of Arizona.
The concession could be a breakthrough, but Senate Republicans were still balking at an agreement, adopting a new argument that Democrats wanted to raise taxes just to increase spending, not to cut the deficit. That concern appeared to center on a Democratic proposal to temporarily suspend across-the-board spending cuts to military and domestic programs as talks resumed on a larger deficit deal.
The demand for the new way of calculating inflation, known as "chained C.P.I.," issued at 7:10 p.m. on Saturday, had stopped talks cold. Senator Mitch McConnell, the Republican leader, went to the Senate floor a little after 2 p.m. on Sunday to say that Republicans had made their last offer and had yet to receive a reply.
"I'm concerned about the lack of urgency. I think we all know we're running out of time," Mr. McConnell said.
Senator Harry Reid, the majority leader, responded that "at this stage, we're not able to make a counteroffer." He said that Mr. McConnell had negotiated in good faith but that "we're apart on some pretty big issues."
Mr. McConnell said he had made an emergency call to Vice President Joseph R. Biden Jr. to get the talks started again. The two spoke twice, and the White House dispatched the president's chief legislative negotiator, Rob Nabors, to the Capitol to meet with Senate Democrats.
Talks foundered after Republicans dug in in an effort to get the largest deficit reduction deal in the time remaining, according to numerous Republican and Democratic officials familiar with the negotiations. Republicans told Democrats that they were willing to put off scheduled cuts in payments to health care providers who treat Medicare patients but that they wanted spending cuts elsewhere.
But it was the inflation calculation that forced Democrats from the negotiating table. President Obama has said that in a "grand bargain" on deficit reduction, he would go along with the change, which would slow the growth of programs whose outlays rise with consumer prices, and would raise more revenue by pushing people into higher tax brackets.
Democrats said that Mr. Obama and Congressional Democrats would accept that change only as part of a larger deal that included locking in well more than $1 trillion in revenue over 10 years, along with other Republican concessions. Democrats fear that any such concessions now would only increase demands for additional compromises in the coming weeks, when talks resume on a "grand bargain" to reduce the deficit.
They point to the $1 trillion in spending cuts agreed to last year in the Budget Control Act. Democrats say those should be included in a $4 trillion "grand bargain," but Republicans say those cuts should not be part of future negotiations. Republicans would likely do the same if Democrats agree now to concessions on the inflation calculation, Democratic aides said Sunday.
Mr. Reid made clear that Democrats did not intend to include Social Security in any stopgap package. Doing so would make it hard for him to round up votes from his own party, and he has resisted touching Social Security.
"We're not going to have any Social Security cuts," Mr. Reid said on the floor.
The breakdown came after Mr. Obama appeared on the NBC program "Meet the Press" on Sunday and implored Congress to act.
"We have been talking to the Republicans ever since the election was over," Mr. Obama said in the interview, which was taped on Saturday. "They have had trouble saying yes to a number of repeated offers. Yesterday I had another meeting with the leadership, and I suggested to them if they can't do a comprehensive package of smart deficit reductions, let's at minimum make sure that people's taxes don't go up and that two million people don't lose their unemployment insurance."
"And I was modestly optimistic yesterday, but we don't yet see an agreement," Mr. Obama said. "And now the pressure's on Congress to produce."
Unless Congress acts by midnight Monday, a broad set of tax increases and federal spending cuts will be automatically imposed on Jan. 1, affecting virtually every taxpayer and government program. The spending cuts were put in place earlier this year as draconian incentives that would force the president and lawmakers to confront the nation's growing debt. Now, lawmakers are trying to keep them from happening, though it seemed likely that the cuts, known as sequestration, would be left for the next Congress, to be sworn in this week.
Both sides worry that the confrontational tone that the president took on "Meet the Press" was not helpful.
Don Stewart, a spokesman for Mr. McConnell, issued a statement criticizing Mr. Obama's remarks. "While the president was taping those discordant remarks yesterday," Mr. Stewart said, "Senator McConnell was in the office working to bring Republicans and Democrats together on a solution. Discussions continue today."
House Speaker John A. Boehner of Ohio, in his comments, pointed to the president as the problem. Republicans have tried to reach an agreement, Mr. Boehner said, but "the president has continued to insist on a package skewed dramatically in favor of higher taxes that would destroy jobs."
Republicans have blamed Mr. Obama for seeking to punish the wealthy with large tax increases and have accused him of not negotiating in good faith. They say his approach would worsen the deficit by protecting Democratic constituency groups from tax increases and benefit reductions while imposing sharp penalties on farmers and small business owners.
Senator John Barrasso of Wyoming, a member of the Republican leadership, said Sunday on the CNN program "State of the Union" that Mr. Obama was not dealing with the real issue imperiling the economy -- the Democrats' "addiction to spending."
The president and party leaders in the House and Senate have been seeking a compromise measure that would protect middle-income families from the worst of the tax increases, but there has been no agreement on where to draw the line. With the Bush-era tax cuts expiring, Mr. Obama and Democrats have said they want tax rates to rise on incomes over $250,000 a year; Republicans want a higher threshold, at perhaps $400,000.
As part of the last-minute negotiations, the lawmakers have haggled over unemployment benefits, cuts in Medicare payments to doctors, taxes on large inheritances and limits on the impact of the alternative minimum tax, a parallel income tax system that is intended to ensure that the rich pay a fair share but that is increasingly encroaching on the middle class.
Mr. Obama has said that if talks between the Senate leaders break down, he wants the Senate to schedule an up-or-down vote on a narrower measure that would extend only the middle-class tax breaks and unemployment benefits. Mr. Reid said he would schedule such a vote on Monday absent a deal.
In his comments, Mr. Obama singled out the top Republican leaders -- Senator McConnell and Speaker Boehner -- for threatening to derail any deal in order to protect the wealthiest Americans.
Under questioning from David Gregory, the host of "Meet the Press," Mr. Obama would not accept any responsibility for the impasse. He blamed Republican intransigence and political "dysfunction" in Washington, and said he had offered multiple reasonable compromises.
"What is it about you, Mr. President," Mr. Gregory asked, "that you think is so hard to say yes to?"
"That's something you're probably going to have to ask them," the president responded, "because, David, you follow this stuff pretty carefully. The offers that I've made to them have been so fair that a lot of Democrats get mad at me."
Mr. Obama said the priority for Republicans seemed to be "making sure that tax breaks for the wealthiest Americans are protected."
At some point, he said, "I think what's going to be important is that they listen to the American people."
Another issue dividing Democrats and Republicans is the tax on inherited estates, which currently hits inheritances over $5 million at 35 percent. On Jan. 1, it is scheduled to rise to 55 percent, beginning with inheritances exceeding $1 million.
This article originally appeared in The New York Times.