DES MOINES, Iowa—Zach Nunn, an Iowa state senator running for Congress, suddenly finds himself flooded with high-profile Republican friends.

The GOP nominee in Iowa’s Third Congressional District has the good fortune of running in the state where the 2024 Republican presidential-nomination race is expected to start. That means that prospective candidates are eager to campaign at his side and help him raise money in what has shaped up as one of the nation’s most competitive U.S. House races.