President Barack Obama will meet with congressional leaders from both parties at the White House Friday afternoon in a bid to revive negotiations to avoid the so-called fiscal cliff, with three days remaining before it's deadline.

The meeting is set for 3 p.m. EST Reuters reports.

Leaders were divided on the odds of success, with a few expressing hope, some talking as if the leaders had abandoned it, and a small but growing number suggesting Congress might try to stretch the deadline into the first two days of January.

The Republican-dominated House of Representatives convened a session for Sunday to be ready to pass a bill if one emerges.

House Majority Leader Eric Cantor, R-Va., advised members to be prepared to meet through Jan. 2, the final day before the new Congress takes office.

It "doesn't feel like anything that's very constructive is going to happen" from the White House meeting, said Sen. Bob Corker, R-Tenn., Reuters reported. "It feels more like optics than anything that's real.”

The parties remained far apart, particularly over Democratic demands to raise tax rates on the richest Americans. But one veteran Republican, Rep. and Sen.-elect Jeff Flake of Arizona, held out the prospect that if Obama came through with significant spending cuts, Republicans in the House might compromise on taxes.

Flake told Reuters that Republicans were resigned to some increases in top income-tax rates, although he did not specify a dollar threshold.

While he wished for no tax rates to go up, Flake said: "I've felt we should've moved a week or two ago to accept the top rate going up and tell the president 'congratulations.'"

The bigger problem in avoiding the cliff, Flake said, would be if Obama demanded cancellation of the $109 billion in automatic spending cuts set to begin Jan. 2 without alternative spending cuts to replace them.

"There will be resistance from a lot of House conservatives to a deal that does that," he said.

Any resolution at this point would be a scaled-back version of the package Obama and congressional leaders had anticipated passing after the election, The Wall Street Journal predicts. The White House is pressing for the Senate to extend current tax rates for incomes of up to $250,000, extend unemployment benefits, keep the alternative minimum tax from hitting millions of additional taxpayers and delay automatic spending cuts -- known as sequestration -- set to take effect in January.

The 11th-hour strategy carries enormous risk because it leaves no margin for error in Congress' legislative machinery. Senate Majority Leader Harry Reid, D-Nev., said the prospects for passage of a bill before year’s end are fading rapidly, the Journal reports. "I have to be very honest," he said. "I don't know time-wise how it can happen now."

At best, leaders are looking at a narrow bill that could be passed at the last minute. At the meeting Friday, Obama will outline the elements he thinks should be in a deal and could get majority support in both chambers of Congress, a person familiar with the matter told the Journal. He won't put forward a specific bill or legislative language, the person added.