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In a briefing after the assault, Brennan got into some hot water for implying that bin Laden was armed -- he was not -- and for suggesting that bin Laden used a human shield -- he did not.

"There was a female who was, in fact, in the line of fire that reportedly was used as a shield to shield bin laden from the incoming fire," Brennan told reporters.

More recently, the White House has been criticized by some Republicans for the leaks of sensitive information on counterterrorism operations that made the administration look good during the presidential campaign. Brennan has called the leaks devastating and vehemently denied that administration officials were involved.

The controversy over leaks, the drone program and his position on the CIA's interrogation and detention program could make for some rough moments during Brennan's confirmation hearings.

The fact he is coming from the West Wing and frequently talked about the president's views on camera could make him political fodder, Frances Fragos Townsend, CNN's national security contributor, told Security Clearance.

"John came out time and again and did a lot of press early on that angered Republicans on (Capitol) Hill," Townsend said. "Do I think Republicans will treat him not as a former career professional? He's got to expect that the Hill is going to treat him as a political person who is fair game now, rightly or wrongly."

None of the former officials and experts CNN spoke to believes Brennan's nomination would be upended by any of the criticisms of him.

Harlow thinks Brennan is a hard-working, no-nonsense type with the experience to run the agency.

"John's the kind of guy who is the catcher on the team that gets all dinged up, takes his hits but gets the job done," Harlow said.