If a deal was not possible, it would become evident at Friday's White House meeting, and Obama and the leaders would leave a resolution for the next Congress to address in January.
Such a delay could unnerve the stock market, which edged lower for a fifth day Friday amid worries that lawmakers would fail to reach a budget deal. Economists say that if the tax increases are allowed to hit most Americans and if the spending cuts aren't scaled back, the recovering but fragile economy could sustain a traumatizing shock.
Obama called for the meeting as top lawmakers on Thursday alternately cast blame on each other while portraying themselves as open to a reasonable last-minute bargain.
Senate Democratic Leader Harry Reid all but conceded that any effort at this late date was a long shot. "I don't know timewise how it can happen now," he said.
The No. 2 Senate GOP leader, Jon Kyl of Arizona, said it is "pretty unlikely" that Senate Republicans would agree to legislation averting the fiscal cliff if it wouldn't pass muster in the House.
"If you know the House isn't going to do something, why go through the charade?" he told reporters. "That becomes political gamesmanship."
Obama and Reid, D-Nev., would have to propose a package that Senate Republican Leader Mitch McConnell would agree not to block with procedural steps that require 60 votes to overcome.
Sen. Chuck Schumer of New York said he still thinks a deal could be struck.
The Democrat told NBC's "Today" show Friday that he believes the "odds are better than people think."
Schumer said he based his optimism on indications that McConnell has gotten "actively engaged" in the talks.