(Update: Even more reason to ask whether Sen. Lieberman will unequivocally rule out accepting a Cabinet appointment from President Bush.)

Bob Woodward confirms that the idea of Sen. Lieberman being appointed Secretary of Defense was more than just a rumor, in an excerpt from his new book, State of Denial, in today's Washington Post:

After President Bush won reelection in 2004, White House Chief of Staff Andrew H. Card Jr. got out an 8 1/2 -by-11 spiral notebook, half an inch thick, with a blue cover. He called it his "hit-by-the-bus" book -- handy in case someone in the administration suddenly had to be replaced. He had intentionally used a student notebook, something he had bought himself, so it wouldn't be considered a government document or presidential record that might someday be opened to history. It was private and personal.

A second term traditionally leads to personnel changes. The question was whether one of them would involve Secretary of Defense Donald H. Rumsfeld....

Card had the names of 11 possible Rumsfeld replacements in his "hit-by-the-bus" book, among them Sen. Joseph I. Lieberman (D-Conn.), who had been Al Gore's vice presidential running mate in 2000 and was a staunch defender of the Iraq war, and Sen. John McCain (R-Ariz.).

And Bush speechwriter Michael Gerson also pushed specifically for Lieberman to replace Rumsfeld in private conversations with the president:

With Card's knowledge and encouragement, Michael Gerson, the chief White House speechwriter, also lobbied the president. Gerson said he believed that Rumsfeld should be replaced, as a symbol of change. The president should talk to Lieberman about taking over for Rumsfeld, Gerson recommended. What better symbol of change could there be than to bring in Gore's running mate?

Knowing how important loyalty was to Bush, he said, "Mr. President, it's not disloyal to have someone in for four years, four and a half years, in a job like this, and then for a variety of reasons, many of them not of his own doing, okay, to say that it would be advantageous to have a change."

Interesting idea, Bush said.