WASHINGTON—When an unpopular Democratic incumbent president was struggling to build support for a second term, a young Delaware senator floated the idea that the party consider other options for the top of the ticket.

“That man’s in trouble, politically in trouble,” Joe Biden said of then-President Jimmy Carter in July 1979, according to an account at the time in the Wilmington Evening Journal. Biden had held off on publicly backing Carter because he wanted to endorse a candidate who would ensure Democrats retained the White House in the 1980 election. “I’m not certain that’s Jimmy Carter right now,” he told the paper.