Democrats indicated some spending cuts would be fine with them. "I feel confident that a solution may be in sight," said House Democratic leader Nancy Pelosi of California.
The goal of the high-pressure talks to come is to produce a multitrillion-dollar deficit-reduction plan that can take the place of the across-the-board tax increases and spending cuts that are slated to take effect on Jan. 1.
In remarks while reporters were present, Obama stressed that time was short as he welcomed the leaders to the White House for the first time since winning re-election this month. "We have urgent business to do," he said.
If nothing else, the mood seemed good around the table in the Roosevelt Room of the White House. Obama noted that it would soon be Boehner's birthday and said he wasn't "going to embarrass him with a cake because we didn't know how many candles were needed."
"Yeah, right," said Boehner, who's turning 63 on Saturday, chuckling as he playfully poked the president in the elbow.
There was no indication that the meeting touched on Obama's campaign-long call to raise tax rates at upper incomes.
In their public comments, neither the president nor the lawmakers dwelt on long-standing differences that doomed previous deficit negotiations. Senate Republican leader Mitch McConnell came closest, telling reporters that while Republicans are willing to discuss increased revenue, most members of his party "believe we are in the dilemma we are in not because we tax too little but because we spend too much."
After the meeting, White House Press Secretary Jay Carney said, "Both sides agreed that while there may be differences in our preferred approaches, we will continue a constructive process to find a solution and come to a conclusion as soon as possible."
For all the expressions of optimism, it was unclear whether the Nov. 6 elections and the prospect of the so-called fiscal cliff would serve as a strong enough catalyst for these talks to succeed where other recent attempts have failed.
Obama ran for a new term calling for a "balanced approach" to deficit reduction that includes raising taxes on income over $200,000 a year for individuals and $250,000 for couples. And while the president has stated a willingness to pull federal savings out of benefit programs including Medicare and Medicaid, Democratic leaders have been reluctant to go along.
Raising taxes has long been anathema to Republicans, who say government's spending must be cut to reduce deficits and taxes reduced to stimulate job creation in an economy where unemployment is 7.9 percent.
Boehner told reporters after Friday's meeting that he had outlined a framework for negotiations that "is consistent with the president's call for a fair and balanced approach." He did not provide details, except to say it "deals with reforming our tax code and reforming our spending," a reference to benefit programs such as Medicare and Medicaid.
An aide said Boehner's approach calls for agreement on long-term revenue and spending targets to be set into law, presumably this year, leaving details to 2013 on an overhaul of the tax code and remaking benefit programs.
"There is no more 'let's do it some other time,'" said Senate Majority Leader Harry Reid, D-Nev. "We're going to do it now. ... We feel very comfortable with each other, and this isn't something we're going to wait until the last day of December to get it done."
Obama favors $1.6 trillion in higher taxes over the next decade, in part by allowing existing cuts to expire on Dec. 31 on higher incomes.
White House officials claim an overall deficit reduction package totaling more than $4 trillion, although that includes $1 trillion in spending cuts agreed to last year, and an additional $1 trillion in spending no longer needed for the wars in Iraq and Afghanistan. Republicans and independent fact checkers dispute the claimed savings from the two wars, since the money was borrowed in the first place.
Whatever the obstacles to a deal, there is little dispute about the cost of failure.
Under current law, tax cuts that took effect more than a decade ago will expire at all income levels at the end of the year, as will Bush-era reductions for investors, married couples, families with children and others. The 2 percent payroll tax cut would end, and an additional 26 million taxpayers would come under the alternative minimum tax.
As well, the defense budget would be cut by $55 billion, and domestic programs would incur a reduction of the same size.
Unemployment benefits for some of the longest-term jobless also expire at the end of the year.
Boehner has said previously that any agreement should include an increase in the national debt limit, now $16.4 trillion. The Treasury is expected to hit that cap sometime in the next few months.