Senate Republicans say Senate Republican Leader Mitch McConnell Addison (Mitch) Mitchell McConnellIn rare move, Schumer forces vote to consider health care bill amid Supreme Court tensions COVID-19 talks hit crucial stretch Supreme Court nominee gives no clues in GOP meeting MORE (Ky.) is willing to drop his demand to curb the growth of Social Security cost-of-living increases.

The demand from McConnell had thrown a wrench into talks Sunday on a “fiscal cliff” deal as Senate Majority Leader Harry Reid Harry Mason ReidGOP senators confident Trump pick to be confirmed by November Durbin: Democrats can 'slow' Supreme Court confirmation 'perhaps a matter of hours, maybe days at most' Supreme Court fight pushes Senate toward brink MORE (Nev.) and other Democrats quickly balked at the request, which they said they would not accept.

ADVERTISEMENT

But a number of Senate Republicans said it was not a core demand of their conference, suggesting taking it out of a deal would not prevent a last-second agreement from being reached.

"We need to take CPI off the table," said Sen. John McCain John Sidney McCainAmerica's presence in Cam Ranh Bay should be more than occasional Meghan McCain, husband welcome first baby girl, Liberty Sage McCain Domenech The Hill's Morning Report - Sponsored by JobsOhio - Showdown: Trump-Biden debate likely to be nasty MORE (R-Ariz.). "That is not part of the negotiations because we can't win an argument that has Social Security for seniors versus taxes for the rich, so we need to take it off the table."

At issue is the formula used to calculate benefit payments. Republicans prefer switching to the chained consumer price index — or "chained CPI" — while Democrats insist on maintaining the current method.

When asked if Republican leaders would be willing to drop Social Security reform from the talks, McCain said: "I think we're in agreement that should be off the table."

Incoming Senate Republican Whip John Cornyn John CornynBig donors fund state parties at record levels Trump, GOP aim to complete reshaping of federal judiciary Fears grow of chaotic election MORE (R-Texas) said Republican leaders never really expected Reid to agree to reduce the growth of the entitlement program in the midst of tax negotiations.

"I don't think anybody ever expected Social Security to be part of this, it's all going to be about taxes," he said.

Cornyn said the biggest obstacle at this point is getting Democrats to return to the talks.

"The discussion was really about the fact that there had been no response to the Republican offer by Sen. Reid and that really we didn't have a negotiating partner," he said, summarizing a closed-door meeting of the Senate GOP conference Sunday afternoon.

Reid said on the Senate floor Sunday evening he will continue working with McConnell and alerted colleagues to expect the next update Monday morning.

“There is still significant distance between the two sides but negotiations continue,” Reid said. “There is still time left to reach an agreement, and we intend to continue negotiations.

“We’ll have further announcements perhaps at 11 in the morning, I certainly hope so,” he said.

McConnell has begun talking with Vice President Biden in an effort to "jump-start" the negotiations.

McConnell left the Republican meeting to speak to Biden by phone and later returned. He told colleagues he needed some time to process what Biden said and come back to them with a recommendation.

Despite the blowup over Social Security, Senate Democrats and Republicans appear to be inching toward an agreement.

Reid has proposed raising the threshold for extending income tax rates to $360,000 for individual income and $450,000 for family income, according to Sens. Dick Durbin Richard (Dick) Joseph DurbinSupreme Court nominee gives no clues in GOP meeting Warren won't meet with Barrett, calling Trump's nomination an 'illegitimate power grab' Conservative group unveils ad accusing liberals of attacking Barrett's faith MORE (D-Ill.) and Tom Harkin Thomas (Tom) Richard HarkinThe Memo: Trump attacks on Harris risk backfiring Ernst challenges Greenfield to six debates in Iowa Senate race Biden unveils disability rights plan: 'Your voices must be heard' MORE (D-Iowa), who with other Democrats received a briefing from Reid. Rob Nabors, the White House director of legislative affairs, attended the meeting but did not speak to the caucus.

Republicans have countered with a proposal to extend rates for individual income below $450,000 on individual income and $550,000 for family income, according to the senators.

Harkin said Republicans also want to set the estate tax rate at 35 percent with an exemption on $5 million inheritances.

“It’s just not good,” he said.

Durbin said Democrats are still fighting to extend unemployment benefits but acknowledged their demand for transportation stimulus is no longer realistic.

Republicans say Democrats have dropped their demand to include an increase in the federal debt ceiling.

Emerging from the Democratic caucus meeting, Reid said he was glad that Republicans are willing to drop Social Security from the mix but added “we’re still left with a proposal they've given us that protects the wealthy and not the middle class, and I'm not going to agree to that."

Both sides are still trying to turn off $109 billion in sequestered cuts to defense and non-defense spending. Democrats want to use the new tax revenue from allowing Bush era rates to expire to offset turning off the sequester, a Democratic aide said. The GOP wanted chained CPI as the offset.

"If that is unacceptable to them, they need to come up with an alternative," Sen. John Thune John Randolph ThuneHouse in near-unanimous vote affirms peaceful transfer of power In rare move, Schumer forces vote to consider health care bill amid Supreme Court tensions Supreme Court nominee gives no clues in GOP meeting MORE (R-S.D.) said.

Democrats and Republicans also disagree over how to pay for stopping the automatic spending cuts.

A senior Democratic aide said the money should come from the revenues collected from raising taxes on the wealthy, but some Republicans say that is unacceptable.

“We all know revenues are going to increase on the wealthy,” said Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.). “To use that money to spend it and not use it to reduce deficits is beyond belief and goes against everything the president has said over the last year but that’s where they are.

“You cannot in my opinion turn the sequester off without paying for it,” he said. “You can’t pay for it with revenues, those are cuts.”

McCain said he would not vote for any deal that does not delay the sequester of defense spending.

Cornyn said that McConnell expects to convene the conference again later Sunday as talks continue.

Without a deal, Reid has said he will bring to the floor on Monday a default bill that extends the Bush-era income tax rates for family income below $250,000, extends unemployment benefits and expiring business tax provisions, and freezes scheduled cuts in Medicare payments to doctors.

A top Senate Republican said the party would likely try to amend Obama's tax proposal if Reid brought it to the floor. Asked if the GOP would demand a 60-vote threshold to pass the president's bill at the last minute, Sen. John Cornyn (Tex.) replied, "We'd like to be able to offer some amendments."

Battles over amendments often delay action on Senate legislation, but a number of Republican senators said Sunday they might vote for Obama's fallback bill if it was the final option to prevent a major portion of the fiscal cliff.

— Russell Berman and Erik Wasson contributed to this report.

— Posted at 4:32 p.m. and last updated at 6:25 p.m.