Ultimately, though, Mr. Obama came to rely on Mr. Clinton, not only as a silver-tongued surrogate, but also as a private counselor. Mr. Obama huddled with Mr. Clinton at the home of the Hollywood mogul Jeffrey Katzenberg just days after the president’s disastrous performance in the first debate with Mr. Romney.

And on election night, immediately after Mr. Romney’s concession call, Mr. Obama instructed his campaign manager: “Get Bill on the phone.”

As the relationship between Mr. Obama and Mr. Clinton thawed during the campaign, the incumbent’s bond with his vice president was tested. On a trip to California in early 2012 dedicated to raising money for Mr. Obama’s campaign, Mr. Biden sought to append some meetings with Silicon Valley and Hollywood heavyweights that could help his future ambitions. Word got back to David Plouffe, a top adviser to Mr. Obama. “We can’t have side deals,” Mr. Plouffe told Mr. Biden. The vice president apologized to the aide.

But after a leak that infuriated Mr. Obama, the president followed Mr. Plouffe’s recommendation to limit the size of their strategy meetings, a decision that excluded Mr. Biden. Mr. Obama and his team were also angry when Mr. Biden declared his support for same-sex marriage on “Meet the Press” in the spring of last year, pre-empting the president’s own poll-tested plans to announce what the book indicates was a position he had held as early as 2004.

As for the Republicans, the book includes details with potential 2016 implications for Mr. Christie, who is widely seen as a favored candidate among establishment Republicans.

Mr. Romney included the blunt-talking governor on his vice-presidential shortlist, crossed him off, reconsidered choosing him and then ultimately decided that he could not pick Mr. Christie. Mr. Romney made the decision not only because of the fund-raising restrictions Mr. Christie would face as the governor of New Jersey, but also because Mr. Christie did not offer the same amount of information to Mr. Romney’s team of vetters as the other potential vice-presidential picks.

According to a memo on Mr. Christie from the vetting team, it had unanswered questions on a defamation lawsuit against the governor from earlier in his political career, on a Securities and Exchange Commission settlement involving Mr. Christie’s brother, on names and documentation of his household help, on information from his time as a securities industry lobbyist, and on his medical history. “The dossier on the Garden State governor’s background was littered with potential land mines,” the authors write.