Woodward is a famed chronicler of presidents, best known for his revelations in the Watergate scandal that proved the undoing of Richard Nixon in 1974.
Trump and the White House, along with numerous senior officials including Defense Secretary James Mattis and chief of staff John Kelly, strongly disputed the book's content. Colbert asked how we can know what's going on when Trump changes his mind daily, or maybe forgets what he thought yesterday.
"These are political statements to protect their jobs", he said. "I remember going to one general's house, he opened the door - we didn't have an appointment, I was afraid I might get shot".
The source, while citing demeaning views of Trump from other unnamed senior officials, declined to say how many officials had actually taken this vow of resistance, or when and how they had taken this vow.
"The things-some of the things-that Trump did and does jeopardizes the real national security", Woodward said.
Throughout the interview, after accusing Trump of waging a "war on the truth", Woodward brought up anecdote after anecdote (all of them second-hand from anonymous sources) to paint a picture of an out-of-touch, almost insane commander-in-chief who is "detached from reality".
Woodward has stood by his reporting despite the White House's response, saying on Sunday that Kelly and Mattis are "not telling the truth" in their denials. "There's too much evidence, too many witnesses".
"He (Modi) told me the United States has gotten nothing out of Afghanistan".
"It doesn't seem to be anybody very high up because everybody very high up has already said, 'It wasn't me, '" Trump said. Both men are accused in the book of effectively removing things from Trump's desk to prevent him from taking certain actions. People know who Woodward is. I mean, to try to control the presidency while not the president.
"We have reprinted six times for a total of seven to meet extraordinary demand - that will put one million books in print before we've even gone on sale", a Simon & Schuster spokesperson said to CNN "Reliable Sources" host Brian Stelter.
"And what you want to do is say, do you have any documents or notes. and they say no, no, no".
The pair fought over Trump's desire to place tariffs on imports, and Cohn is said to have stolen documents off Trump's desk to prevent the president from pulling the U.S. out of major trade deals.