The aides concluded that despite Mrs. Clinton’s popularity, the move would not offer a significant enough political boost to Mr. Obama to justify such a radical move, according to a newly published account of the 2012 race.

The idea of replacing Mr. Biden with Mrs. Clinton had long been rumored, but the journalists Mark Halperin and John Heilemann, in their new book, “Double Down,” provide a detailed description of the effort inside the senior circle of Obama advisers. It was pushed by the chief of staff at the time, William M. Daley, despite the close personal rapport Mr. Daley had developed with Mr. Biden, a fellow Irish Catholic and veteran of Washington politics.

“When the research came back near the end of the year, it suggested that adding Clinton to the ticket wouldn’t materially improve Obama’s odds,” the authors write in their sequel to “Game Change,” which chronicled the 2008 campaign. “Biden had dodged a bullet he never saw coming — and never would know anything about, if the Obamans could keep a secret.”