“I hear so much about that from people up here. And you know, we’re gonna build a wall."

He talked about the heroin-addiction epidemic in the state, a major issue that voters at almost every rally seem affected by, in one way or another.

“I hear so much about that from people up here,” Mr. Trump said. But then he pivoted to a familiar refrain: “And you know, we’re gonna build a wall. We’re gonna have a real border.”

And therein is the problem for Mr. Trump, who is losing ground in Iowa to Senator Ted Cruz of Texas even as he consistently tops polls in New Hampshire. But Mr. Trump faces a field of people vying to be the establishment candidate, including Gov. Chris Christie of New Jersey, Senator Marco Rubio of Florida, Jeb Bush and Gov. John R. Kasich of Ohio. Mr. Trump is an exceptional political performer who, by now, could have developed a message beyond his core, and no front-runner can risk two straight losses.