David A. Kaplan wrote that Souter made the comment while discussing the matter in private with a group of prep school students.
Souter said if he had "one more day one more day," he could have convinced Kennedy to vote with the dissenters and Congress might have been charged with handling the controversy.
The book, titled "The Accidental President," is previewed in the Sept. 17 issue of Newsweek magazine. Kaplan says the book will dissect how the government handled the 2000 election, which came down to who won Florida.
President Bush was declared the winner over Al Gore 36 days after the voting, following the Supreme Court decision that effectively halted a partial recount in Florida.
For part of the book, Kaplan focuses on Souter, who wanted Congress to decide what to do.
"While a political resolution to the election might not be quick and might be a brawl, Souter argued that the nation would still accept it," Kaplan wrote. Souter tried desperately to get Kennedy to vote with the minority, according to the book, but he wouldn't flip.
"He thought the trauma of more recounts, more fighting more politics was too much for the country to endure," Kaplan wrote.
The book also reveals that several of the judges had a spat in front of several Russian judges during an exchange program meeting after the vote.
Kaplan wrote that during a meeting, a Russian judge criticized the nation for letting judges choose the president.
Tempers flared and Justice Stephen Breyer said the decision was "the most outrageous, indefensible thing the Court has ever done," according to Kaplan.
Kennedy answered, "Sometimes you have to be responsible and step up to the plate," according to the book. Justice John Paul Stevens offered, "I'm so tired. I am just so exhausted."
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