By Richard Cowan

WASHINGTON (Reuters) - While Republican leaders in the House of Representatives insist that raising tax rates on the rich is an impossibility, some Republican lawmakers now see it as inevitable to avoiding the "fiscal cliff" of severe tax hikes and spending cuts set to start January 1.

Congressional aides, who asked not to be identified, said Republicans are losing the public relations battle over keeping low tax rates for the rich and are getting battered by President Barack Obama and his fellow Democrats in Congress following their November 6 election victories.

On Capitol Hill aides often play an important role of communicating what members are thinking but cannot say themselves. In recent days, increasing numbers are putting out word through news organizations that Republicans now feel they cannot win on tax cuts for the wealthy, at least not now.

Without a deal by December 31, $600 billion in across-the-board spending cuts and tax increases, which are so severe that they likely would shove the economy into recession, are scheduled to begin.

Republican Senator Bob Corker of Tennessee told reporters that his fellow Republicans are beginning to see a possible upside to giving in to Obama on tax rates so the party can then try to gain the upper hand in subsequent negotiations - maybe next year - to make savings in expensive "entitlement" programs such as Medicare healthcare for the elderly.

"If the House were to give that to him, where does the discussion then go? It goes to entitlements, which is where it ought to be in the first place," said Corker, who added, "I'm hearing whispers of a light going off in some people's minds."

Conservative Republican Senator Tom Coburn of Oklahoma told MSNBC: "Personally I know we have to raise revenue. I don't really care which way we do it. Actually, I would rather see the rates go up than do it the other way because it gives us a greater chance to reform the tax code and broaden the base in the future."

Democrats on Wednesday kept up pressure on Republicans to allow votes on legislation to continue low tax rates on everyone with net incomes below $250,000 a year - an estimated 98 percent of taxpayers. Rates for the 2 percent above that threshold would snap back to pre-2001 levels of 35 percent and 39.6 percent under a Senate-approved bill.

"The first step, the most obvious step, is for the Republican House to take the 98 percent both sides agree on and pass our Senate bill and send it to the president for his signature," Democratic Senator Patty Murray of Washington state said in excerpts to a speech she was to deliver on the Senate floor later on Wednesday.

A Senate Republican aide noted that Republicans "are in a very weak bargaining position" on maintaining low tax rates of 33 percent and 36 percent on the top two income brackets "and we all know we are going to get hell if we go off the cliff."

The aide saw the possibility of Republicans and Democrats swapping a few more proposals that they know will be rejected, before moving to an end-game by mid-December or so.

One such Republican proposal, according to another Republican aide, would set forth a $1.6 trillion deficit-reduction plan, with half the savings coming from higher revenues and the other half from tough entitlement program cuts - meaning benefit reductions for the elderly and poor that Democrats undoubtedly would oppose, at least for now.

THE REAL DEAL?

But the real proposal - one that would be presented to the full House and Senate for passage this month - could involve letting tax rates rise on the highest income earners, although maybe not to as high a level as Obama is demanding, according to aides. It could be coupled with extending low estate taxes and protecting middle-income people from being thrown into a tax level intended for the rich.

The deal also would set up a framework, which has been widely discussed, to work on comprehensive tax and spending reforms next year that ultimately could reduce all tax rates while ending a broad swath of tax breaks.

The Senate Republican aide added that if there is no deal to avert the fiscal cliff by December 31, Republicans would find themselves in an even worse position in the new Congress convening in January.

Senate Democrats will have a larger majority next year, having picked up two more seats as a result of the November 6 elections. The party also has gained seats in the House.

"We know that if we wait until the new Congress, the 98 percent bill will get passed by the Senate and there will be more pressure in the House to do it by discharge," the Senate Republican aide said.

"Discharge" refers to attempts already underway by House Democrats to get the Democratic bill extending tax cuts for everyone but the rich to the House floor through a "discharge petition" signed by a majority of the chamber's members.

Even amid all the speculation of a Republican-Democratic deal in coming weeks, it is hard to find anyone who voices complete confidence in such an outcome, leaving open the possibility that the country can still go off the fiscal cliff on January 1.

(Additional reporting by Kim Dixon and Thomas Ferraro; Editing by Fred Barbash and Vicki Allen)