WASHINGTON: The current flare-up between Republican National Committee Chairman Michael Steele and popular right-wing radio talk show host Rush Limbaugh has many wondering who is leading the Republican Party.

The verbal pushing contest between Steele and Limbaugh also has many in the Republican Party uncomfortable with the attention the spat has caused politically.

Steele appeared over the weekend on CNN, where he fought back against the assertion that radio host Rush Limbaugh was the "de facto leader" of the Republican Party. Steele said he himself was the de facto leader and called Limbaugh "an entertainer" whose program's content was "incendiary" and "ugly".

Then Limbaugh shot back, saying on his show that Steele was not the leader of the party and that many conservatives would "hang up" when Steele's RNC called for contributions.

Steele later said he had reached out to Limbaugh to clarify his remarks, insisting he meant no offense. But the incident elicited crowing from Democrats, who for weeks have pursued a strategy seemingly designed to elevate Limbaugh to the front of the GOP line.

But Steele's efforts to appease appeased few: "The new Republican Party chairman Steele is getting slapped around, not just by liberals but by many in his own party. Steele's mishandling of Rush Limbaugh -- first calling him 'incendiary' and 'ugly,' then making a groveling apology -- has turned him into this week's piñata, wrote Howard Kurtz Thursday in The Washington Post.

"In fact, when Steele refused to appear on (MSNBC's)'Morning Joe' yesterday, Scarborough cracked: 'Did Rush not give him permission?'"

Conservatives feel that Steele's highly visible position has caused such embarrassment that is calling for his resignation.

In an e-mail to fellow RNC members obtained by The Hill newspaper, Ada Fisher, North Carolina's national committeewoman, said Steele is "eroding confidence" in the GOP and that members of his transition team should encourage him to step aside.

Fisher's call for Steele's resignation comes amid growing frustration in the GOP that the new chairman's repeated gaffes are hurting the party.

Calling the Limbaugh-Steele clash a "Republican Horror Show," Fisher expressed what some other GOP strategists have until now only said privately: "I have never seen such ineptness in our GOP leadership," Fisher wrote. "And I thought we handled the 2008 elections very poorly."

As for Rush Limbaugh, his saga took another turn when the bellicose broadcaster challenged President Barack Obama to a debate.

Limbaugh's listeners know that he likes to "push the envelope" for the sake of entertainment and ratings, but his visceral attacks on Obama have helped focus the Democrats attacks against him after Limbaugh said he hoped President Barack Obama "fails" at a gathering of conservative political activists last weekend.

Keeping the momentum going, Limbaugh said Wednesday: "Let's talk about the New Deal versus Reaganomics," after inviting Obama to stop by. "Let's talk about closing Guantanamo Bay, and let's talk about sending $900 million to Hamas. Let's talk about illegal immigration and the lawlessness on the borders."

Limbaugh said that, since last fall, the White House "led by Rahm Emanuel, the chief of staff to Barack Obama, has been targeting me, your host, your harmless, lovable little fuzzball."

But even conservatives seem to be getting annoyed with Limbaugh's antics.

"It's been fun debating whether the GOP leadership vacuum is being filled by Rush Limbaugh, but I think Rudy Guiliani said it best this morning on CNN: Rush is a powerful voice within the party, but he is not a leader of the party. Leadership is completely different from what Rush does. Both have their place," wrote the conservative Dallas News.

"Rush seems way out of his element challenging a sitting president to a talk show debate. Aren't Republicans the same ones who think Democrats don't show enough respect for the office? Don't they bemoan Obama's shirtsleeves attire in the Oval Office? And yet they think he should be bullied into a talk show appearance to debate economics with an entertainer? Give me a break ... Rush's ego seems to be the only thing growing faster than Obama's budget deficit."