Spokesmen for both sides said they agreed to not release details of the conversation.
“The lines of communication remain open,” the White House and Mr. Boehner’s office said in identical statements afterward.
Just hours before the meeting, a key Republican senator suggested that his party should perhaps accede to Mr. Obama’s demand to raise the top tax rates so attention can shift to making serious cuts in benefit programs such as Medicare and Medicaid.
Sen. Bob Corker (R., Tenn.) said on Fox News Sunday that a small but growing group of Republicans had begun considering acquiescence on tax rates so the talks could shift to entitlements.
Mr. Corker, a member of the Banking Committee, said that if Republicans gave in to the President’s chief demand, then “all of a sudden, the shift goes back to entitlements, and maybe it puts us in a place where we actually can do something that really saves the nation.”
Republicans have been insisting that the Obama Administration agree to substantial savings in entitlement programs as the two sides negotiate how to narrow the nation’s huge deficits.
But Mr. Corker is among a group of Republicans who say that the party will have to yield to the Obama demand of higher tax rates for top earners, potentially back to the levels that prevailed under President Bill Clinton.
That group of Republicans, he said on Fox, was realizing “that we don’t have a lot of cards as it relates to the tax issue before year-end” — but that a tax-rate concession could be converted into a tactical advantage.
He made the comments as key figures on network news programs mixed cautious words of optimism with dire warnings about what a failure to act might bring.
Christine Lagarde, the managing director of the International Monetary Fund, warned that such a failure was the gravest threat now facing the U.S. economy — greater than the European debt crisis or any uncertainty in China.
“It would result in the stock market really taking a hit,” she said on CNN’s State of the Union. The result could be zero growth next year, not the 2.1 percent growth rate projected by the IMF.
She called for a “balanced” agreement of revenue increases and spending cuts. That is a word Mr. Obama has often used to describe his preferred outcome.
Ms. Lagarde offered a tentative prediction that what she called American “pragmatism” would prevail.
Sen. Charles Schumer of New York, the No. 3 Senate Democrat, also predicted that a deal would be reached. He said he thought it would include a stipulation that the national debt ceiling be raised, without further drama, when it comes due in late January or February.
“I believe, frankly, our Republican colleagues have learned that to say the government is not going to pay its debts and hold it up for something else is bad substance and bad politics,” he said on Fox News Sunday. “I don’t think they’ll prevail on that.”
Mr. Corker agreed with Mr. Schumer that “we’re not going to go over the fiscal cliff.” But he suggested that Republicans would not so easily give up on the debt-ceiling leverage.
“Republicans know that they have the debt ceiling that’s coming up right around the corner, and the leverage is going to shift,” he said.
A Senate vote is required to raise the nation’s statutory borrowing limit.
One author of the much-disputed Simpson-Bowles debt-reduction plan, the former Wyoming Sen. Alan Simpson, a Republican, expressed some optimism Sunday.
He said he thought a deal would be reached but that if it were too narrow — if it failed to make deep enough cuts in health-care spending or other big social programs — the economy, and Americans, would still suffer.
“I’m an optimist,” he said on the CBS program Face the Nation. “I think they’ll do something, but if they do small ball, that won’t work: The markets aren’t going to listen to that.”
His partner in the plan, Erskine Bowles, who was White House chief of staff under Mr. Clinton, warned that a failure in the talks would be “disastrous.”
But he said he was somewhat more upbeat than he was a week ago because of signs of movement from both sides.
After weeks of what he called “kabuki theater,” the two sides have “started to tango now,” Mr. Bowles said on CBS. Asked if a deal could be reached by the end of the year, he replied, “They absolutely can do it. If they don’t do it, shame on them.”