It says that, at one point, Cheney even got in the president's face, as the vice president relentlessly pressed Mr. Bush about it.
"These last hours represent a climactic chapter in the mysterious and mostly opaque relationship at the center of a tumultuous period in American history," the report says. "It reveals how one question - whether to grant a presidential pardon to a top vice-presidential aide - strained the bonds between Bush and his deputy and closest counselor."
Libby was convicted of obstructing the investigation of the 2003 outing of former CIA operative Valerie Plame. Her name was revealed to reporters after her husband, former Ambassador Joseph Wilson, criticized the Bush administration's prewar intelligence on Iraq.
The leak led to a long probe that resulted in Libby's conviction on charges of obstruction of justice and lying to investigators. Mr. Bush commuted Libby's sentence, and Llibby never served prison time, but the president didn't pardon him.
Cheney appealed to the president several times, Time says. During Mr. Bush's final week in office, Cheney was as determiend as ever to clear Libby's name and wouldn't relent, the magazine adds.
"Cheney really got in the president's face," a family source told Time, which also interviewed dozens of anonymous White House insiders. "He just wouldn't give it up."
In response to the Time article, Cheney said, "Scooter Libby is an innocent man who was the victim of a severe miscarriage of justice. He was not the source of the leak of Valerie Plame's name. Former Deputy Secretary of State, Rich Armitage, leaked the name and hid that fact from most of his colleagues, including the President. Mr. Libby is an honorable man and a faithful public servant who served the President, the Vice President and the nation with distinction for many years. He deserved a presidential pardon."
On "The Early Show Saturday Edition," Time assistant Managing Editor Michael Duffy explained that Libby was the "vice president's top aide, long-time adviser on both domestic and foreign policy, and he got in trouble with the law. What we find fascinating is ... that the vice president pressed President Bush three times for this pardon. And even after the president had decided it once, twice, and with some finality, it kept coming back up.
"That was an interesting insight - a window into this relationship that was really the most important in the last ten years in our country, and not very well-reported, a hard-to-read, transparent, opaque, kind of very difficult relationship to understand, and this is the really first time anyone climbed into their back-and-forth.
"I think everyone on both staffs, the vice president's staff and the president's, realized this was coming to a head in a potentially very volatile way," Duffy continued. "Everyone was quite nervous about it; both sides took fairly hard positions. The president at one point told his own personal lawyer that, if he had to take a poll on whether to give Libby a pardon, it would be 100-1 against in his staff.
"And so, by the time the Bush White House is coming to a close in the final three or four days, it's really kind of both sides are at loggerheads with each other. And in the end, Bush would just have to give the news to the vice president himself."
Did Mr. Bush have concerns that Cheney wasn't being completely honest in insisting Libby had nothing to do with the leak?
"I think there was some concern deep down among some in the White House," Duffy told co-anchor Chris Wragge. "We quote people saying, 'Even we weren't entirely sure what the deal was between Cheney and Libby.' But I think Bush decided not to do it because he didn't feel Libby was remorseful and he felt that he had in fact broken the law.
"What's interesting is that, since they've left office, this is another place where the two men have gone separate ways, (with ) Bush retiring fairly quietly to Texas, and Cheney staying in the fray here (in Washington)."
Asaid Mr. Bush refused to send troops to arrest possible terror suspects in a Buffalo, N.Y. suburb in the aftermath of 9/11 - an unlawful use of military force within the United States that was purportedly supported by Cheney. Wragge wondered whether we're gong to see "maybe a long line of decisions that Vice President Cheney wanted President Bush to make that President Bush ended up not making."
"I think," Duffy responded, "we're both going to discover that they had differences on all sorts of things. ... But they also maintained such a tight and disciplined ship during their eight years. We didn't find out about them then.
"We are beginning to find out about them now."