On CBS News's Face the Nation Sen. Joe Biden, D-Del, the ranking Democrat on the Foreign Relations Committee, said he thinks Rumsfeld should lose his job because of what he sees as mismanagement of the war.
Biden also said that, in an Oval Office meeting, he told President Bush and Vice President Dick Cheney that he wanted Cheney to step down for the same reasons.
"The present said to me, quote, 'Why do you keep picking on Rummy?' I looked at the president, and I said, 'Mr. President, with all due respect' – and I looked at the vice president – 'Mr. Vice President, I would call for your resignation as well, were you not a constitutional officer,'" Biden told host Bob Scheiffer.
"And the president said, 'Why would you say that?' And I said, 'Mr. President, not one piece of advice either Don Rumsfeld or Dick Cheney has given you has turned out to be correct with regard to Iraq.' And the president just seems completely wedded to the notion," Biden said.
Biden said that the president has to change the course in Iraq. Despite the presence of more than 600,000 troops in the war-torn nation, violence is increasing.
But when Schieffer asked if Biden thinks the vice president should resign, Biden said no.
"I was making the point that these guys just don't know what they're doing," he said. "And no one takes them seriously anymore except the president, apparently."
Woodward's book claims that former White House chief of staff Andrew Card and First Lady Laura Bush.
Appearing on the show after Biden, White House counselor Dan Bartlett said the president still has confidence in Rumsfeld.
"He's the right man to do this job. It's a very difficult job. There are a lot of armchair quarterbacks, but he's the right man," he said.
Also in Woodward's book is the revelation that two months before the Sept. 11 attacks, then-CIA director George Tenet asked for an emergency meeting with Secretary of State Condoleezza Rice, who was then serving as National Security Adviser. The CIA feared an attack was coming by al Qaeda.
According to Woodward, this meeting was not mentioned in testimony before the 9/11 Commission.