(CBS) Cheney stunned Woodward by revealing that a frequent advisor to the Bush White House is former Secretary of State Henry Kissinger, who served Presidents Nixon and Ford during the Vietnam War.

"He’s back," Woodward says. "In fact, Henry Kissinger is almost like a member of the family. If he’s in town, he can call up and if the president’s free, he’ll see him."

Woodward recorded his on-the-record interview with Cheney, and here’s what the vice president said about Henry Kissinger’s clout: "Of the outside people that I talk to in this job I probably talk to Henry Kissinger more than just about anybody else. He just comes by and I guess at least once a month," Cheney tells Woodward. "I sit down with him."

Asked whether the president also meets with Kissinger, Cheney told Woodward, "Yes. Absolutely."

The vice president also acknowledged that President Bush is a big fan of Kissinger.

"Now, what’s Kissinger’s advice? In Iraq, he declared very simply:
'Victory is the only meaningful exit strategy.' This is so fascinating. Kissinger’s fighting the Vietnam War again. Because in his view the problem in Vietnam was we lost our will. That we didn’t stick to it," Woodward says.

He says Kissinger is telling the president to stick to it, stay the course. "It’s right out of the Kissinger playbook," Woodward says.

In his book, published by CBS sister company, Simon & Schuster, Woodward reports that the first President Bush confided to one of his closest friends how upset he is that his son invaded Iraq.

"The former President Bush is said to be in agony, anguished, tormented by the war in Iraq and its aftermath," Wallace says.

"Yes," Woodward replies.

Asked if the former president conveys that message to his son, Woodward says, "I don’t know the answer to that. He tells it to Brent Scowcroft, his former national security advisor."

"You paint a picture, Bob, of the president as the cheerleader-in-chief. Current reality be damned. He’s convinced that he’s gonna succeed in Iraq, yes?" Wallace asks.

"Yes , that’s correct," Woodward says.

Woodward interviewed President George W. Bush for the first two books for hours.

"And do you know what? There are people who are gonna say, look Woodward is savaging President Bush because he wouldn’t see him for this book," Wallace remarks.

Woodward says that's not true. "He did not, and I asked. And I made it very clear to the White House what my questions were, what my information was. What could he say? That the secret chart is not right?" Woodward says. "That these things that happened in these meetings didn’t occur? They’re documented. I talked to the people who were there. Your producer, Bob Anderson, has listened to the tapes of my interviews with people to make sure that it’s not just kind of right, but literally right. This is what occurred."

And Woodward says that no matter what has occurred in Iraq, Mr. Bush does not welcome any pessimistic assessments from his aides, because he’s sure that his war has Iraq and America on the right path.

"Late last year he had key Republicans up to the White House to talk about the war. And said, 'I will not withdraw even if Laura and Barney are the only ones supporting me.' Barney is his dog," Woodward says. "My work on this leads to lots of people who spend hours, days with the president."

"And in most cases they are my best sources. And there is a concern that we need to face realism. Not being the voice that says, 'Oh no, everything’s fine,' when it’s not," Woodward adds.

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