(Repeats to fix typo in "Republican" in 8th paragraph)

* Cheney calls investigation bad for national security

* McCain concerned about effect on CIA morale

WASHINGTON, Aug 30 (Reuters) - Former Vice President Dick Cheney said he might refuse to speak with a prosecutor investigating suspected CIA prisoner abuses, a probe he branded as political and bad for national security.

Cheney has been one of the fiercest critics of U.S. Attorney General Eric Holder's decision last week to name a new special prosecutor to look deeper into harsh interrogations of captured terrorism suspects during the Bush administration.

Asked whether he would talk to prosecutor John Durham if eventually sought out, Cheney told "Fox News Sunday": "It will depend on the circumstances and what I think their activities are really involved in. I've been very outspoken in my views on this matter."

The cases under investigation include a mock execution, use of a power drill to scare a prisoner and the waterboarding of accused Sept. 11 mastermind Khalid Sheikh Mohammed 183 times.

"I'm very proud of what we did in terms of defending the nation for the past eight years, successfully," Cheney said in a recorded interview. "And it won't take a prosecutor to find out what I think. I've already expressed those views."

Cheney said he did not know at the time which methods were used in specific cases but defended the interrogators, saying "the enhanced interrogation techniques were absolutely essential in saving thousands of American lives."

The decision to name a prosecutor could create political headaches for President Barack Obama and distract lawmakers from his drive to overhaul the U.S. healthcare system.

On Sunday, Republican lawmakers renewed their concerns about the investigation while one of Obama's key allies sought to distance the president from Holder's decision.

Democratic Senator John Kerry said he believed "there's a little bit of a tension between the White House itself and the lawyers and the Justice Department.

"And in a sense, that's good, that's appropriate, because it shows that we have an attorney general who is not pursuing a political agenda but who is doing what he believes the law requires him to do," Kerry told ABC's "This Week."

Prominent Republicans including Senator John McCain, a former presidential candidate and torture survivor during the Vietnam War, said they were concerned about the investigation's impact on morale at the CIA.

A Washington Post report on Sunday cited former intelligence officials saying CIA morale was sagging.

"I worry about the morale and effectiveness of the CIA," McCain told CBS's "Face the Nation." "I worry about this thing getting out of control and us harming our ability to carry on the struggle that we're in with radical Islamic extremism."

Senator Diane Feinstein, a Democrat who chairs the Senate Intelligence Committee, said she understood Holder's decision but questioned why he did not wait for her committee to finish a bipartisan investigation.

"I think the timing of this is not very good. The intelligence committee has under way now a total look at the interrogation and detention techniques used for all of the high-value detainee," Feinstein told CBS.