On Sunday, International Monetary Fund chief Christine Lagarde echoed numerous economic experts in predicting a sharp drop in confidence and "zero" U.S. economic growth if there's no agreement.
The tax issue was a main November election campaign topic, with Obama saying the wealthiest Americans must pay more and Republicans opposing any tax rate increase.
Four polls in the past two weeks, including a new one released Monday, show that more Americans support Obama's proposal.
The Senate has passed a measure that holds down tax rates on income below $250,000 for families, as sought by Obama, while letting rates go up to 1990s levels for higher earners.
Obama and Democrats say House passage of that proposal would clear the way for a broader deal. However, House Republicans refuse to bring it up for a vote amid cracks in the GOP facade against a rate hike.
Sen. Bob Corker of Tennessee said Sunday that he would support raising taxes on the top 2% of income earners, arguing that it will better position Republicans to negotiate for larger spending cuts to Social Security and Medicare despite opposition from many Democrats.
"A lot of people are putting forth a theory, and I actually think it has merit, where you go ahead and give the president ... the rate increase on the top 2%, and all of a sudden the shift goes back to entitlements," Corker said on "Fox News Sunday."
Fellow Republican Sens. Tom Coburn of Oklahoma and Susan Collins and Olympia Snowe of Maine also have said they could vote for such a limited tax hike.
On the House side, Rep. Tom Cole of Oklahoma reiterated Sunday that he could go along with higher rates on the wealthy.
"You have to do something, and doing something requires the cooperation of the Senate, which the Democrats run, and the signature of the president," he said on CNN's "State of the Union."
Meanwhile, conservative colleague Rep. Marsha Blackburn of Tennessee refused to budge from GOP orthodoxy against higher tax rates.
Even though Obama won re-election and Democrats increased their Senate majority while narrowing the Republican majority in the House, she insisted that the November vote showed that voters "clearly said we don't want our taxes to go up."