Let’s remember this section from Bob Woodward’s book State of Denial:
[Andrew] Card kept pushing, at one point raising the possibility of change at the Pentagon with Vice President Cheney.
No, Cheney said, he was predisposed to recommend that the president keep Rumsfeld right where he was. Card was not surprised.
In private conversations with Bush, Cheney said Rumsfeld’s departure, no matter how it might be spun, would be seen only as an expression of doubt and hesitation on the war. It would give the war critics great heart and momentum, he confided to an aide, and soon they would be after him and then the president. He virtually insisted that Rumsfeld stay.