WASHINGTON - President Barack Obama and Republican House Speaker John Boehner met Sunday at the White House to discuss the ongoing negotiations to avert the impending "fiscal cliff," as a growing number of Republicans in Congress appear to be moving toward acceptance of Obama's demand that tax rates go up on the wealthy.

It was the first meeting between just the two leaders since Election Day, Nov. 6. Spokesmen for both Obama and Boehner said they agreed to not release details of the conversation, but emphasize that the lines of communication remain open.

The meeting comes as the White House and Congress try to break an impasse over finding a way to avert the so-called "fiscal cliff," a combination of automatic tax increases and spending cuts scheduled to kick in at the beginning of next year.

Obama met in November with Boehner, as well as Senate Majority Leader Harry Reid and House Minority Leader Nancy Pelosi. The president spoke separately by telephone with Reid and Pelosi on Friday.

Obama has been pushing higher tax rates on the wealthiest Americans as one way to reduce the deficit — a position Boehner and other House Republicans have been steadfastly against. Republicans are demanding steeper cuts in costly entitlement programs like government health insurance and pension payments for older Americans.

One Republican senator said Sunday that Senate Republicans would probably agree to higher tax rates on the wealthiest Americans if it meant getting a chance to overhaul entitlement programs.

Tennessee Sen. Bob Corker said on Fox television Sunday that he speaks for many Republicans who realize that Obama holds the stronger hand on increasing taxes on the wealthy in the ongoing debate about how to avoid sending the U.S. economy over the so-called "fiscal cliff." Many economists and the non-partisan Congressional Budget Office predict that failure to solve the political standoff would push the fragile American economy back into recession.

The fiscal cliff faces the country because tax rate cuts that were put in place during the former President George W. Bush administration expire at the end of the year. Obama campaigned during his successful run for a second term on keeping the cuts in place for all but the top two per cent of American earners. Republicans want to find additional government income by cutting back on tax loopholes and deductions while leaving the tax rates unchanged.

The pending across-the-board reductions in government spending, impacting everything from social programs to the military, were put in place last year as an incentive to both parties to find spending reductions to begin cutting government red ink. That legislation grew out of the two parties' inability in 2011 to agree to a tax and spending program that would have taken a big bite out of the deficit.

Compounding the likely devastating effects of failure to agree on a means of avoiding the fiscal cliff will be the coincidental expiration of extended government benefits for the long-term unemployed.

The remarks by Corker, who is building a reputation as a pragmatic deal maker among fiscally conservative Republicans, and support among a growing number of colleagues in Congress put fresh pressure on Boehner and others in the Republican caucus to rethink their long-held assertion that even the very rich shouldn't see their rates go up next year. Republican leaders have argued that the revenue gained by hiking the top two tax rates would do little to reduce the government budget deficit and would only harm job creation.

But Corker says insisting on that red line — especially since Obama won re-election after campaigning on raising tax rates on the wealthy — might not be wise.

"There is a growing group of folks looking at this and realizing that we don't have a lot of cards as it relates to the tax issue before year end," Corker said.

If Republicans agree to Obama's plan to increase rates on the top 2 per cent of Americans, Corker said, "the focus then shifts to entitlements and maybe it puts us in a place where we actually can do something that really saves the nation."

Besides getting tax hikes through the Republican-dominated House, Corker's proposal faces another hurdle: Democrats haven't been receptive to the opposition party's proposals on entitlement programs. Sen. Dick Durbin, the No. 2 Senate Democrat, was skeptical about proposals to increase the eligibility age for Medicare, the government health insurance program for the elderly, from 65 to 67. He said on NBC television he doesn't see Congress addressing the complicated issue of Medicare overhaul in the three weeks remaining before the end of the year.

"I just don't think we can do it in a matter of days here before the end of the year," Durbin said. "We need to address that in a thoughtful way through the committee structure after the first of the year."

Among those moving toward accommodation on higher tax rates for the wealthy is Republican Rep. Tom Cole of Oklahoma, who has said Obama and Boehner should agree not to raise tax rates on the majority of Americans and negotiate the rates for top earners later. Cole said Sunday that most House Republicans would vote for that approach because it doesn't include a rate hike.

"You know, it's not waving a white flag to recognize political reality," Cole said.

Sen. Tom Coburn, an Oklahoma Republican, already has said he could support higher tax rates on upper incomes as part of a comprehensive plan to cut the federal deficit.

When asked on ABC television Sunday what it would take to sign on to a tax rate increase, Coburn echoed Corker's comments by responding: "Significant entitlement reform." He quickly added, however, that he has estimated that Obama's proposed tax rate increase for the wealthy would only affect about 7 per cent of the deficit.

"Will I accept a tax increase as a part of a deal to actually solve our problems? Yes," Coburn said. "But the president's negotiating with the wrong people. He needs to be negotiating with our bondholders in China, because if we don't put a credible plan on the discussion, ultimately, we all lose."

Still hard-line fiscal conservatives in the House of Representatives are holding fast to their position.

"No Republican wants to vote for a rate tax increase," said Rep. Jeb Hensarling of Texas, chairman of the House Republican Conference.

Obama's plan would raise $1.6 trillion in revenue over 10 years, partly by letting decade-old tax cuts for the country's highest earners expire at the end of the year. He would continue those Bush-era tax cuts for everyone except individuals earning more than $200,000 and couples making above $250,000. The highest rates on top-paid Americans would rise from 33 per cent and 35 per cent to 36 per cent and 39.6 per cent.

Boehner has offered $800 billion in new revenues to be raised by reducing or eliminating unspecified tax breaks used by upper-income people. The Republican plan would cut spending by $1.4 trillion, including by trimming annual cost-of-living increases in Social Security payments and raising the eligibility age for Medicare.

Hensarling and Coburn spoke on ABC's "This Week." Cole spoke on CNN's "State of the Union." Durbin spoke on NBC's "Meet the Press."