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A leading Republican came out against the front-runner for CIA director, Gen. Michael Hayden, saying Sunday the spy agency should not have military leadership during a turbulent time among intelligence agencies.

Members of the Senate committee that would consider President Bush's nominee also expressed reservations, saying the CIA is a civilian agency and putting Hayden atop it would concentrate too much power in the military for intelligence matters.

Bush was expected to nominate a new director as early as Monday to replace Porter Goss, who abruptly resigned on Friday.

But opposition to Hayden because of his military background is mounting on Capitol Hill, where he would face tough hearings in the Senate Intelligence Committee.

Despite a distinguished career at the Defense Department, Hayden would be "the wrong person, the wrong place at the wrong time," said the chairman of the House Intelligence Committee, Rep. Peter Hoekstra, R-Mich.

"There is ongoing tensions between this premier civilian intelligence agency and DOD as we speak," Hoekstra said. "And I think putting a general in charge — regardless of how good Mike is — ... is going to send the wrong signal through the agency here in Washington but also to our agents in the field around the world," he told "FOX News Sunday."

But Sen. John McCain, R-Ariz., said other military members have been head of the CIA, a position that he called "the toughest job in Washington."

"This is a very important and key post and I hope [lawmakers] will recognize that General Hayden is a very qualified individual and he is the president's selection," McCain said on CBS' "Face the Nation." "General Hayden is more of an intelligence person than he is an Air Force officer."

If Hayden were to get the nomination, military officers would run the major spy agencies in the United States, from the ultra-secret National Security Agency to the Defense Intelligence Agency.

The Pentagon already controls more than 80 percent of the intelligence budget.

"You can't have the military control most of the major aspects of intelligence," said Democratic Sen. Dianne Feinstein of California, who is on the Senate Intelligence Committee. The CIA "is a civilian agency and is meant to be a civilian agency," she said on ABC's "This Week."

A second committee member, GOP Sen. Saxby Chambliss of Georgia, added, "I think the fact that he is a part of the military today would be the major problem."

Sen. Joe Biden, D-Del., mentioned fears the CIA would "just be gobbled up by the Defense Department" if Hayden were to take over.

The chairman of the Senate Judiciary Committee said he would view a Hayden nomination as a way to get information from the Bush administration about its secretive domestic surveillance program, undertaken by the NSA when Hayden led that agency.

The warrantless monitoring covered electronic communications between people in the United States and other parties overseas with suspected terrorist links.