WASHINGTON (Reuters) - U.S. Republicans who have long dominated American politics find themselves fighting with each other for a way out of the wilderness after losing the last two elections to Barack Obama’s Democrats.

Michael Steele speaks after being elected Republican National Committee chairman in Washington January 30, 2009. REUTERS/Molly Riley

A feud between conservative talk radio king Rush Limbaugh and the Republicans’ new national party chairman, Michael Steele, is emblematic of the distance the party has to go to achieve dominance once again.

Laughing from the sidelines are President Obama’s White House and the Democratic Party, eager to inflict further political pain by baldly declaring Republicans “the party of Limbaugh,” a reference to the polarizing man who is beloved by conservatives but viewed with skepticism by many others.

Leading Republicans are engaged in a “what do we do now” debate as they seek a way to rehabilitate their image in the age of Obama.

Before Obama was elected in November, Republicans had been in charge of the White House for 28 of the last 40 years.

So far, party elders are trying to steer the party back to its roots by demonstrating fiscal responsibility and fighting Obama’s major increases in government spending -- an objective that faltered during Republican George W. Bush’s presidency.

They also see a desperate need to increase the appeal of the Republican Party beyond its white, Southern base. This was part of the thinking behind the choice of Steele, who is the first African-American to be elected party chairman.

Minnesota Governor Tim Pawlenty, a Republican in a Democratic-leaning state and often mentioned as a possible contender in the 2012 presidential race, told Reuters the party should have three main goals:

“Number one, the idea factory has grown stale. We need new leaders with new ideas. Number two, we need to do a better job of convincing younger voters, female voters, diverse voters of why they should support Republicans or conservatives,” Pawlenty said.

“Number three, I think we have to communicate in a more modern and contemporary fashion. That includes being more optimistic and more hopeful.”

Pawlenty said Republicans may benefit from what he described as Democrats “overplaying their hand.”

The idea is that Democrats flush with power -- holding the White House and the Congress -- are seeking to force Americans into liberal spending and social policies that they do not support, and that Republicans will benefit from the backlash.

“We may be a beneficiary of them overreaching. But that itself is not a vision for the future of our party and our country. We don’t want to be just a beneficiary of luck,” Pawlenty said.

INCENDIARY AND UGLY

Limbaugh drew a rebuke from Steele by telling conservatives last weekend in Washington that he wanted Obama to fail “if his mission is to restructure and reform this country so that capitalism and individual liberty are not its foundation.”

Steele declared subsequently to CNN that Limbaugh’s comments were incendiary and ugly, prompting Limbaugh to question Steele’s ability to lead the party.

Steele eventually apologized to Limbaugh in an acknowledgment of his power as a popular radio host, but not before Republicans were complaining about him.

“Steele won the party’s chairmanship five weeks ago,” said Republican strategist Scott Reed.

“He fired the entire staff. Who’s running the place? Who’s raising the money, recruiting the candidates, designing the voter identification programs and helping work with the congressional wing to design a message? Who’s doing all this work? No one.”

The dust-up was only one of many challenges the Republicans are encountering.

A young up-and-coming Republican, Louisiana Governor Bobby Jindal, was widely mocked for his televised response to Obama’s speech to a joint session of Congress last week.

Jindal, 37, an Indian-American, had an uninspired performance, relating party platitudes in a speech delivery that was widely panned.

“I hope people look at the content of the speech, not just the delivery. You know, for years, I’ve been told I speak too quickly. Now I’m told I speak too slowly,” Jindal told CNN’s “Larry King Live.”

Republican strategist Ron Kaufman said Republicans need to be able to work with Obama when they consider him right but be respectfully against him when they think he is wrong, such as in the debate over the $787 billion economic stimulus bill that Republicans opposed.

“To me, the new cool is competent. And the way for us to come back is to prove to the American voters that we are the party of competence,” Kaufman said.