Majority leader Harry Reid and Republican leader Mitch McConnell gave a relatively upbeat assessment after the duo and top House leaders had what McConnell called a "good" meeting with Mr Obama.
"I am hopeful and optimistic" of reaching an agreement after months of gridlock, Mr McConnell said.
He said he hoped for a compromise that could be presented to politicians by tomorrow, little more than 24 hours before the year-end deadline.
Mr Reid said, "I'm going to do everything I can" to make a deal happen. He cautioned, "Whatever we come up with is going to be imperfect."
Success was far from guaranteed in an atmosphere of mistrust -- even on a slimmed-down deal that postponed hard decisions about spending cuts into 2013. Congressional Democrats said Mr Obama was ready with a revised offer to present.
But that drew a denial from a person familiar with the talks, who said the president would review his proposal from a week ago, when he urged lawmakers to preserve tax cuts for most while letting rates rise above incomes of $250,000 a year.
At the same time, Mr Obama said politicians should extend unemployment benefits for the long-term jobless. The person was unauthorised to discuss the private meeting publicly and spoke on condition of anonymity.
For Mr Obama, the 11th-hour scramble represented a test of how he would balance strength derived from his re-election against an avowed commitment to compromise in the face of divided government.
The stock market was down again yesterday amid the developments in Washington.