(USATODAY.com) - The House reconvened Monday in a rare New Year's Eve session and the Senate was set to follow suit, but all the action on a possible "fiscal cliff" deal remained behind closed doors as Vice President Joe Biden and top Senate Republican leader Mitch McConnell worked late into the night to in an effort to avoid a midnight deadline.
Without an agreement, a series of tax hikes and spending cuts are set to begin taking effect on Tuesday.
McConnell and Biden "continued their discussion late into the evening (Sunday) and will continue to work toward a solution," said McConnell spokesman Don Stewart, pledging "more information as it becomes available."
Senate Majority leader Harry Reid, D-Nev, who was also heavily involved in the talks, was expected to speak at 11 a.m. ET with an update on talks.
Optimism rose and fell throughout Sunday as officials from Capitol Hill to the White House dickered over budget details, worked the phones, spoke with reporters - and generally blamed each other for the impasse over a deal to avert higher taxes on all Americans, massive cuts to major programs and a possible recession as a result.
From Capitol Hill on Monday morning, Sen. Tom Coburn, (R-Okla.) told MSNBC'sMorning Joe program that most lawmakers, who are not among the small group of negotiators, were sitting around the Capitol building listening to pundits on television.
"Something has gone terribly wrong when the biggest threat to our American economy is the American Congress," said Sen. Joe Manchin, D-W.Va.
After Senators failed Sunday to come up with a bipartisan proposal on a deal, the White House served notice it may push its own plan and dare Republicans to oppose it.
The pared-down plan would include a renewal of unemployment insurance and an extension of the George W. Bush tax cuts for middle-class Americans who make less than $250,000 a year.
"Republicans will have to decide if they're going to block it, which will mean that middle-class taxes do go up," President Obama said on NBC's Meet The Press.
Sunday began with the Obama's interview on NBC in which he said he remained hopeful of a deal, but made it clear he would hold Republicans responsible if the nation goes over the fiscal cliff.
"The way they're behaving is that their only priority is making sure that tax breaks for the wealthiest Americans are protected," Obama said.
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Republicans pointed the finger right back at Obama.
House Speaker John Boehner, R-Ohio, said Obama has always emphasized tax hikes ahead of spending cuts, especially when it comes to the fast-rising entitlement programs of Social Security and Medicare.
"Americans elected President Obama to lead, not cast blame," Boehner said in a statement.
On the Senate floor, McConnell said he called Vice President Biden "to see if he could help jump-start negotiations on his side." The Republican leader noted that he and Biden have worked well together during previous budget battles.
The two "continued their discussion late into the evening (Sunday) and will continue to work toward a solution," said McConnell spokesman Don Stewart, pledging "more information as it becomes available."
As Reid adjourned the Senate early Sunday evening, he said, "We are apart on some pretty big issues."
During the negotiations, McConnell said, "I'm concerned with the lack of urgency here. There's far too much at stake.
"There is no single issue that remains an impossible sticking point," he said. "The sticking point appears to be a willingness, an interest or courage to close the deal."
In one sign of movement, Republicans dropped a demand to slow the growth of Social Security and other benefits by changing how those payments are increased each year to allow for inflation.
Once again, the conflict between the Democratic president and the Republican House has shadowed a budget dispute.
It happened during the near-government shutdown in the spring of 2011. It happened again that same year when the government nearly defaulted during a dispute over the debt ceiling.
As in those previous disputes, the fiscal cliff talks revolve around taxes and spending cuts that could help reduce a federal debt that exceeds $16 trillion.
Obama and the Democrats have emphasized higher tax rates on the wealthiest Americans. Republicans have balked at tax hikes and emphasize spending cuts instead.
Despite their opposition, Republicans pretty much expect that taxes on wealthier Americans are going to rise.
"The president won. The president campaigned on raising rates, and he's going to get a rate increase," Sen. Lindsey Graham, R-S.C., told ABC. But "this deal won't affect the debt situation."
In his NBC interview, taped Saturday, Obama said he has offered Republicans a concession that would reduce Social Security spending by changing the way cost-of-living increases are calculated.
Obama's aides proposed an agreement that would reduce the deficit by $2.4 trillion over 10 years, about half in spending cuts.
"The offers that I've made to them have been so fair that a lot of Democrats get mad at me," Obama said.
Managing the fiscal cliff is essential to improving the economy, the president said. The nation is poised to improve economic growth in 2013, he said, "but what's been holding us back is the dysfunction here in Washington."
Sen. Tom Coburn, R-Okla., said, "We're stuck because many in Congress want to move toward Clinton-era tax rates but not Clinton-era spending."
The president did not make a public appearance Sunday, instead monitoring events from inside the White House.
He did sign one bill: a five-year extension of the Foreign Intelligence Surveillance Act.
Contributing: Associated Press