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"It's the first time that I feel it's more likely that we will go over the cliff than not," Senator Joe Lieberman, an independent from Connecticut, said on CNN's "State of the Union."
"If we allow that to happen it will be the most colossal consequential act of congressional irresponsibility in a long time, maybe ever in American history," Lieberman added.
The Democratic president and Republican House of Representatives Speaker John Boehner, the two key negotiators, are not talking and are out of town for the Christmas holidays. Congress is in recess, and will have only a few days next week to act before Jan. 1.
On the Sunday news shows, no one signaled a change of position that could form the basis for a short-term fix, despite a suggestion from Obama on Friday that he would favor one.
The focus was shifting instead to the days following Jan. 1 when the lowered tax rates dating back to the George W. Bush administration will have expired, presenting Congress with a redefined and more welcome task that involves only cutting taxes, not raising them.
"I believe we are," going over the cliff, said Republican Senator John Barrasso of Wyoming. "I think the president is eager to go over the cliff for political purposes. I think he sees a political victory at the bottom of the cliff," Barrasso said on Fox News Sunday.
Some Republicans have said Obama would welcome the fiscal cliff's tax increases and defense cuts, as well as the chance to blame Republicans for rejecting deal. Obama has rejected that assertion.
Congress started the clock ticking in August of 2011 on the cliff. The threat of about $600 billion of spending cuts and tax increases was intended to shock the Democratic-led White House and Senate and the Republican-led House into bridging their many differences to approve a plan to bring tax relief to most Americans and curb runaway federal spending.
Economists say the harsh tax increases and budget cuts from the fiscal cliff could thrust the world's largest economy back into a recession, unless Congress acts quickly to ease the economic blow.
MARKETS COULD TUMBLE
The most immediate impact could come in financial markets, which have been relatively calm in recent weeks as Republicans and Democrats bickered, but could tumble without prospects for a deal.
Markets will be open for a half-day on Christmas Eve, when Congress will not be in session, and will be closed on Tuesday for Christmas.
Wall Street will resume regular stock trading on Wednesday, but volume is expected to be light throughout the week with scores of market participants away on a holiday break.
If Congress fails to reach any agreement, income tax rates will go up on just about everyone on Jan. 1. Unemployment benefits, which Democrats had hoped to extend as part of a deal, will expire for many as well.
In the first week of January, Congress could scramble and get a quick deal on taxes and the $109 billion in automatic spending cuts for 2013 that most lawmakers want to avoid.
Once tax rates go up on Jan. 1, it could be easier to keep those higher rates on wealthier taxpayers while reducing them for middle- and lower-income taxpayers. Lawmakers would not have to cast votes to raise taxes.
Some lawmakers expressed guarded hope that a short-term deal on deficit-reduction could be reached in the next week or so, with a longer more permanent deal hammered out next year.
But a short-term deal would need bipartisan support, as Obama has said he would veto a bill that does not raise taxes on the wealthiest Americans.
Democratic Senator Kent Conrad, chairman of the Budget Committee, said Obama and Boehner are not that far apart and that both sides should keep pushing for a long-term big deal.
"I would hope we would have one last attempt here to do what everyone knows needs to be done, which is the larger plan that really does stabilize the debt and get us moving in the right direction," Conrad of North Dakota told Fox News.