California is shaping up as a showdown between Hillary Clinton and Sen. Bernie Sanders, with Tuesday’s primary threatening to prevent Mrs. Clinton from a strong finish to the long primary season that would make it easier for her to unify the party ahead of the general election.

Mrs. Clinton cut short a campaign swing this week in New Jersey, where she is favored in its Tuesday primary, so that she could spend more time stumping in California. The campaign also announced on Wednesday that her husband, former President Bill...