Journalist Michael Wolff's latest book, Landslide details the events that led to the deadly Capitol riot on 6 January, and includes an account of how Mr Trump came to believe that Mr Pence could simply overturn the election for him.
The segment of the book detailing Mr Giuliani's alleged false claims was published in New York Magazine on Monday.
Wolff claims in his book that many of Mr Trump's officials and staffers had put distance between themselves and the then-president ahead of the riot, though a small retinue, including Mr Giuliani, continued to meet regularly and offer advice.
According to Wolff, this was when Mr Giuliani began telling Mr Trump that the vice president had the authority not to certify the electoral college votes during the 6 January count.
"There is no question, none at all, that the VP can do this. That's a fact. The Constitution gives him the authority not to certify. It goes back to the state legislatures," Mr Giuliani reportedly told Mr Trump repeatedly.
Wolff claimed that Mr Giuliani was "drinking heavily and in a constant state of excitation, often almost incoherent in his agitation and mania" ahead of 6 January.
Despite his certainty, Mr Giuliani was incorrect in his assumptions about the extent of Mr Pence's power.
The 6 January count is not a certification, but simply a count of the votes submitted by the states. The process does not provide the vice president with any special power to overrule or reject those counts. Individual lawmakers may raise objections – as Senator Ted Cruz and other Republicans attempted to do – but none of that power rests in the hands of the vice president.
Mr Trump apparently bought Mr Giuliani's story; The New York Times reported earlier this year that the then-president told Mr Pence that "You can either go down in history as a patriot, or you can go down in history as a pussy."
Mr Trump even promoted the false idea that Mr Pence could overturn the election with a tweet.
"The Vice President has the power to reject fraudulently chosen electors," Mr Trump wrote.
That was not correct.
The New York Times reported that Mr Pence sat down with Mr Trump after he made the tweet and explained that he did not have the power to reject electors. Mr Trump denied that the discussion took place.
During the attack on the Capitol on 6 January, when some in the mob were chanting “Hang Mike Pence!” and others had set up a mock gallows – and while, inside the building, security had led the vice president to safety – Mr Trump doubled down, tweeting: “Mike Pence didn’t have the courage to do what should have been done to protect our Country and our Constitution.”
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