WASHINGTON – Top congressional leaders emerged from a meeting with President Obama at the White House on Friday trying to project bipartisan confidence that they would manage to break through gridlock and reach consensus and avert a potential economic catastrophe triggered by budget cuts and increased taxes.

President Obama summoned the four top leaders of the House and the Senate – House Speaker John Boehner and Senate minority Leader Mitch McConnell, both Republicans, and House minority leader Nancy Pelosi and Senate Majority Leader Harry Reid, both Democrats – for an hourlong session this morning in the White House.

When they emerged, the four leaders stood by one another, spoke into microphones outside the West Wing, and each took turns calling the meeting “very constructive.”

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“It was good,” Pelosi said. “I feel confident that a solution may be in sight.”

Both sides seem to be looking at the same sheet music – Republicans now concede that they will agree to increase tax revenues, and Democrats saying they will agree to spending cuts – but it’s still an open question over whether they will in the end agree to sing the same song.

There are still major disagreements over whether tax rates will rise for the wealthiest Americans. Obama has insisted that he wants rates for families making $250,000 or more to return to Clinton-era levels, which means they would go from 35 percent to 39.6 percent. Republicans have adamantly opposed any changes to the rates, saying they instead want to close loopholes or limit tax deductions.

Congressional aides will now turn to the difficult task of trying to hammer out a deal. President Obama is heading on a four-day diplomatic trip to Asia on Saturday, and Congress is in recess all next week. But negotiators plan to meet through the week, with proposals to be presented to the principal leaders after the Thanksgiving holiday. Pelosi said a deal should be in place before Christmas.

Boehner said that he presented a “framework” that would both cut spending and reform the tax code.

“To show our seriousness, we’ve put revenue on the table as long as it’s accompanied by significant spending cuts,” Boehner said. “And while we’re going to continue to have revenue on the table, it’s incumbent for my colleagues to show the American people that we’re serious about cutting spending and solving our fiscal dilemma.”

An aide later said that Boehner called for tax and entitlement reform to be tackled over the next year, since the issues are too complex to solve over the course of the next few weeks. Instead, he wants the agreement to include specific targets for savings and for tax reform changes, with details to be worked out later.

Washington has been gripped with the drama over how they will avoid a looming fiscal cliff. If no deal is made, tax rates for everyone will return to the levels there were at in 2001, before President George W. Bush signed a series of tax cuts. There will be deep cuts in federal spending, including military cuts.

In the aftermath of the election – which occurred just 11 days ago – both sides have been posturing and outlining their own pre-bargaining positions. Obama has demanded that any deal include $1.6 trillion in tax increases for the wealthiest Americans, something Republicans oppose.

Republicans say they are willing to make tax code changes that would result in higher payments for the wealthy, but they are more focused on cutting costs among the large entitlement programs such as Medicare, Medicaid, and Social Security.

But the bitter divisiveness that broke into the open during the last round of fiscal talks – when Obama and Boehner failed to come to a “Grand Bargain” while raising the debt limit last year – was removed from the day.

“We had a very constructive meeting,” Boehner said at the outside. “I think it was a very constructive meeting,” Reid said. A few seconds later, Pelosi, too, declared, “It was a very constructive meeting.”

Speaking last, McConnell said, “I can only echo the observations of the other leaders that it was a constructive meeting.” White House spokesman Jay Carney later released a statement saying it was a “constructive meeting” and added, “we will continue a constructive process.”

The negotiations come at a vital time, and could set the tenor for the start of Obama’s second term, and whether it will be marked by more acrimony or will set the stage for a series of bipartisan agreements. Republicans lost seats in the House and Senate, and were unable to win the White House. But they still control the House chamber, and have the numbers needed to stop legislation in the Senate.

Obama so far has been more assertive than he was during past negotiations, pledging that he would not agree to any deal that allows tax rates for the wealthy to stay as they are currently. He is also preparing to take his campaign outside Washington in the coming weeks, trying to use his election win as a rallying cry.

“That’s an agenda that Democrats and Republicans and independents, people all across the country share,” Obama said at the beginning of the Friday meeting. “So our challenge is to make sure that 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.”

“My hope is this is going to be the beginning of a fruitful process that we’re able to come to agreement that will reduce our deficit in a balanced way,” he added.

Just as the meeting began, when reporters were ushered in for photos, Obama remarked playfully that Boehner’s birthday is Saturday.

“We didn’t make him a cake because we didn’t know how many candles we’d need,” Obama said.

As they laughed and shook hands, Boehner, who is turning 63, said, “Yeah, right.”

Obama later gave Boehner a bottle of Tuscan red wine.