Rush Limbaugh may not run the Republican Party, but no one wants to irritate his audience former New York City Mayor Rudy Giuliani (R) acknowledged in an interview Thursday morning.

"They are not wanting to irritate his audience, and Rush is making the most of this," Giuliani said this morning on CNN, discussing the skirmishes between Limbaugh and the White House and RNC Chairman Michael Steele. "This is like a dream for a radio talk show host."

"You have to contain or keep the base of the Republican Party, and you have to expand it," Giuluani, a rumored 2010 gubernatorial candidate, added. "And to the extent that Rush Limbaugh energizes the base of the Republican Party, he's a very important voice."

Still, the former New York mayor, argued that Limbaugh does not speak for the GOP, and that a number of voices -- including Steele -- represent the Republican brand.

Giuliani also broke with Limbaugh by making clear he hopes President Obama succeeds as president. (Limbaugh has controversially said he hopes Obama does not succeed in office.) Giuliani did say, though, that Obama has pursued the "wrong game plan" for success on the domestic economy.

Watch a video of the interview here: