Congressional leaders voiced optimism Friday about reaching a deficit-reduction deal to avert the "fiscal cliff," giving the stock market a reason to rebound from earlier losses.
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They expressed confidence they could reach a deal before Christmas.
The Dow Jones Industrial Average erased its 60 point loss after leaders from both parties appeared on the White House lawn following the meeting.
(Read More: Stocks End Higher, but Dow Logs 4-Week Loss.)
Though no details were disclosed, both sides appeared willing to give ground on the contentious issues of raising taxes and cutting spending.
"I believe we can do this and avert the fiscal cliff," Republican House Speaker John Boehner told reporters on the White House lawn after the leaders met with President Barack Obama.
Democratic Senate Majority Leader Harry Reid was equally upbeat. "We feel we understand what the problem is," he said. "And I feel very good about what we were able to talk about in there."
He said lawmakers will meet with the president again after Thanksgiving.
Rep. Nancy Pelosi, the top Democrat in the House, said she "feel confident that a solution may be in sight."
White House Press Secretary Jay Carney said Obama and the legislative leaders "agreed to do everything possible to find a solution." Carney said White House officials will continue the talks as Obama travels to Asia. Obama leaves on Saturday for a trip that will include a historic stop in Myanmar.
After the meeting, Boehner and Senate Minority Leader Mitch McConnell said they offered higher tax revenue as part of a deal. Boehner said he outlined a framework that is consistent with Obama's call for a "balanced" approach of both higher revenue and spending cuts.
"To show our seriousness, we put revenue on the table, as long as it's accompanied by serious spending cuts," Boehner said.
In offering conditional backing for new revenue, McConnell said reforms to social safety net programs also are necessary.
"We fully understand that you can't save the country until you have entitlement programs that fit the demographics of changing America in the coming years," the Senate minority leader said. "We're prepared to put revenue on the table provided we fix the real problems."
The meeting marked the first time Obama, a Democrat, sat down with his Republican opposition since he won re-election last week.
All eyes were on Boehner, who will have to balance the wishes of a newly confident president with the demands of his rank-and-file conservatives.
The hour-long talks began with Obama calling for "tough compromises."
"My hope is that this is going to be the beginning of a fruitful process where we are able to come to an agreement that will reduce our deficit in a balanced way, that we will deal with some of these long-term impediments to growth, and we're also going to be focusing on making sure that middle class families are able to get ahead," Obama said, sitting next to Boehner.
"Our challenge is to make sure that, you know, we are able to cooperate together, work together, find some common ground, make some tough compromises, build some consensus to do the people's business," he said.
The session was not expected to yield much in the way of tangible results, but it could create a template for the coming weeks of negotiations. And it began on a jovial note. Obama noted that the talks were being conducted a day before Boehner's birthday.
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"We're not going to embarrass him with a cake, because we didn't know how many candles were needed," Obama said. Boehner is turning 63.
And after the meeting, Reid said: "We have the cornerstone of being about to work something out."
Market futures had indicated a higher open Friday after The Wall Street Journal reported White House officials were in discussions that could indicate increased flexibility in negotiations with Republicans. (Read More: White House in Talks to Replace Sequester: Report.)
Citing sources familiar with the matter, the Journal said officials were in advanced, internal talks to replace spending cuts set to begin in January with a separate package of spending cuts and tax increases. The White House had no comment on the report.
Business leaders say uncertainty about the crisis is already weighing on the economy as employers postpone hiring and capital expenditures until they get a better sense of the tax and spending environment.
Investors worry that if no deal is reached on the large, automatic budget cuts and tax hikes set to begin next year, the economy could slip into recession.
"This is the first time we've had one iota of anything constructive being done,'' said Todd Schoenberger, managing principal at the BlackBay Group in New York. "That's very positive, but you can be flexible and still have us go over the cliff. Wall Street traders remain very nervous and need something concrete to get done.''
Both sides are pledging cooperation even as they dig in on their long-held opening positions, and are eager to reassure nervous investors that they will reach a deal.
"Going over the fiscal cliff, in my view, is a bucket of crazy,'' Republican Rep. Peter Roskam, one of Boehner's deputies, said at a budget conference.
Obama insists that tax rates on the wealthiest 2 percent of Americans must rise, while Republicans pledge that they will not agree to any rate increase.
There could be room for compromise.
Obama could agree to allow the top tax rate to rise to something less than the 39.6 percent he wants, from the current 35 percent.
Policymakers, for example, could also agree to limit the tax increase to households making more than $500,000 annually, rather than the $250,000 cap Obama is demanding.
Republicans have suggested generating more revenue by limiting tax breaks for the wealthiest, rather than raising their rates.
Obama has said that would not raise enough money.
The negotiators also need to confront $109 billion in domestic and military spending cuts due to kick in on Jan. 2, the result of earlier failures to craft a more nuanced budget deal.
A senior Democratic Senate aide said it should be relatively easy to head off the cuts, known as "sequestration,'' if the two sides can get past the tax issue.
"The hard part is the tax cuts,'' the aide said. "Neither side wants sequestration to take place, and that should be easy to solve in a balanced plan that has revenues.''
Nonpartisan budget forecasters say failure to reach a deal could push the U.S. economy back into recession and drive up the unemployment rate.
The two sides could also agree to a temporary deal that would get them past the cliff and give them more time to work out a more lasting solution.
White House economic adviser Gene Sperling said the Obama administration is not interested in a solution that simply extends current provisions into next year.
"Compromise cannot be a dirty word if we want to move our country forward,'' Sperling said at a budget conference.
Lawmakers hope to revamp the tax code and retool expensive entitlement programs like Medicare, the government health insurance program for the elderly and disabled.
—Reuters and AP contributed to this report.