At the same time, Senate Majority Leader Harry Reid said that asking wealthier people to pay higher taxes needs to be part of any solution to the government's budget woes.
The Nevada Democrat told reporters in Washington he's "not for kicking the can down the road" and that any solution should include higher taxes on "the richest of the rich."
The fiscal cliff is the one-two punch of expiring Bush-era tax cuts and across-the-board spending cuts to the Pentagon and domestic programs that could total $800 billion next year, based on Congressional Budget Office estimates.
It's is the most immediate item confronting President Barack Obama and a divided Congress in a post-election lame duck session. Economists say it threatens to push the economy back into recession if Obama and Republicans can't forge a deal to prevent it.
"The vast majority of the American people — rich, poor, everybody agrees — the richest of the rich have to help a little bit," Reid said.
The election victory has given Obama new leverage in the upcoming showdown with House Republicans controlling over fiscal issues.
But a rejuvenated Obama still confronts a re-elected House GOP majority that stands in powerful opposition to his promise to raise tax rates on upper-bracket earners, although House Speaker John Boehner, R-Ohio, has left the door open for other forms of new revenue as part of a deal to tackle the spiraling national debt.
"The American people have also made clear that there is no mandate for raising tax rates," Boehner said Tuesday night. "What Americans want are solutions that will ease the burden on small businesses, bring jobs home, and let our economy grow. We stand ready to work with any willing partner — Republican, Democrat, or otherwise — who shares a commitment to getting these things done."
The Ohio Republican is scheduled to address the issue Wednesday afternoon.
Reid also said he anticipates addressing the need to increase the government's borrowing cap early next year and not in the post-election session of Congress.