“He gets very, very little credit, and I think that’s too bad because we got quite a bit of help,” said Dick Moore, Elkhart’s mayor the past eight years, a Democrat who lost election to a third term in November. “I don’t know what we would have done without it.”

Instead, it is Mr. Trump who is making the impression. The New York billionaire routinely attacks Carrier Corporation since it announced in February that it would close two Indiana factories and shift about 2,000 heating and air-conditioning jobs to Mexico. Recently a high school basketball game west of here drew national attention after students hoisted Trump signs and taunted “Build that wall!” at fans from the rival, heavily Latino school.

Many workers remain discouraged. Around Elkhart, “People still don’t feel like they’re doing well,” said Mike Perez, a director at Faith Mission, which provides meals for the poor and shelter for about 150 who are homeless. Many earn less than before the recession, he said. “There still isn’t a sense that everything’s O.K.”