Bernie Sanders’s campaign manager says the Vermont senator will have a difficult time winning the Democratic nomination for president if the same people who typically vote in primaries show up at the polls.

Faiz Shakir, who runs Mr. Sanders’s campaign, told The Wall Street Journal that the lawmaker’s path to both the nomination and the presidency “is the most ambitious and the most difficult path of any candidate” because it relies on support from voters who haven’t been active in the nominating process previously.

“It...