(WASHINGTON) -- With less than one day remaining for Congress to reach a budget agreement that would avoid the so-called "fiscal cliff," a senior White House official tells ABC News that President Obama is still "modestly optimistic" that a deal can be struck to prevent middle class taxes from increasing on New Year's Day.
Senate Majority Leader Harry Reid adjourned his chamber just before 6 p.m. Sunday, ensuring a potential deal could not be voted on before senators return to business Monday morning.
The Nevada lawmaker vowed despite the recess, the parties' leadership would continue negotiations throughout the night.
Vice President Joe Biden has now re-emerged as a key player, and is back in Washington playing "a direct role" in trying to make a deal with Senate Republicans. Biden has been tapped because of his long-standing relationship with Senate Republican Leader Mitch McConnell.
A Democratic source says that McConnell seems to be genuinely interested in getting an agreement. The news dovetails with reports that the GOP has backed off a key Social Security measure that had stalled negotiations.
According to sources, the row was sparked when the GOP offered a proposal that included a new method of calculating entitlement benefits with inflation. Called the "Chained Consumer Price Index," or Chained CPI, the strategy has been criticized by some Democrats because it would lower cost of living increases for Social Security recipients.
"We thought it was mutually understood that it was off the table for a scaled-back deal," a Democratic aide said. "It's basically a poison pill."
Obama has floated Chained CPI in the past as part of a grand bargain, despite opposition from the AARP and within his own party.
Also in the Republican plan brought on Sunday: An extension of the current estate tax and no increase in the debt ceiling. Higher income earners would see their taxes increase, but at levels "well above $250,000," the sources said.
That "major setback" in the talks was evident on the floor of the Senate Sunday afternoon.
"I'm concerned about the lack of urgency here, I think we all know we are running out of time," McConnell said. "I want everyone to know I am willing to get this done, but I need a dance partner."
McConnell, R-Ky., said he submitted the Republican's latest offer to Reid, D-Nev., at 7:10 p.m. Saturday and was willing to work through the night. Reid promised to get back to him at 10 Sunday morning, but has yet to do so.
Why have the Democrats not come up with a counteroffer? Reid admitted it himself moments later.
"At this stage we're not able to make a counteroffer," Reid said, noting that he's had numerous conversations with Obama, but the two parties are still far apart on some big issues. "I don't have a counteroffer to make. Perhaps as the day wears on I will be able to."
McConnell said he believes there is no major issue that is the sticking point but rather, "the sticking point appears to be a willingness, an interest, or frankly the courage to close the deal."
Reid said late Sunday afternoon that the fiscal cliff negotiations were getting "real close" to falling apart completely.
"At some point in the negotiating process, it appears that there are things that stop us from moving forward," he said. "I hope we're not there but we're getting real close and that's why I still hold out hope that we can get something done. But I'm not overly optimistic but I am cautiously optimistic that we can get something done."
Reid said there were serious differences between the two sides, starting with Social Security. He said Democrats are not willing to cut Social Security benefits as part of a smaller, short-term agreement, as was proposed in the latest Republican proposal.
"We're not going to have any Social Security cuts. At this stage it just doesn't seem appropriate," he said. "We're open to discussion about entitlement reforms, but we're going to have to take a different direction. The present status will not work."
Reid said that even 36 hours before the country could go over the cliff, he remains "hopeful" but "realistic," about the prospects of reaching an agreement.
"The other side is intentionally demanding concessions they know we are not willing to make," he said.
The two parties met separately at 3 p.m. Sunday, and before going in, Reid said he hoped there would be an announcement to make on a way forward afterwards. But as of Sunday evening there was no agreement and no counterproposal.
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