DUBUQUE, Iowa — Almost exactly four years ago, Donald J. Trump touched down at an airport hangar here, delivered a donation to a group that provides service dogs to veterans and, before inviting a few kids to run around on his Boeing 757, criticized the wars in the Middle East that many local families had sent their sons and daughters to fight in.

“I’m the guy that didn’t want to go to war,” he told a crowd of several hundred. “It’s just unjust, it’s a mess,” Mr. Trump went on, promising that if he ever did deploy the military anywhere, it would be “so strong, so powerful that nobody is going to mess with us anymore.”

That November, Dubuque County voted Republican in the presidential election for the first time since 1956, when Dwight Eisenhower was on the ballot.

Mr. Trump’s success in places like Dubuque — heavily white, working class, union-friendly and Catholic — remade the Republican electorate. And his path to a second term depends heavily on whether those voters turn their backs on the Democratic Party again.