“The economy is really struggling,” Mr. Dickhut said. “The last eight years, it’s been an abortion.”

Parts of Long Island are also ripe territory for Mr. Trump’s attacks on illegal immigration, an issue that remains potent here. Republicans here readily acknowledge that immigration has had a transformative effect on their communities and, for some longtime residents, an unsettling one.

So many Salvadorans have moved to the Long Island town of Brentwood in recent decades that the country has a consulate there. Debates over day laborers, some of them illegal immigrants, have rived towns and villages throughout the island. Last fall, a federal judge struck down a law in the wealthy Nassau County town of Oyster Bay aimed at stopping day laborers from gathering in public places to seek work.

Rudy Weber, a real estate developer who was strolling through Oyster Bay last week, said he was leaning toward Mr. Trump because he saw him as “an extreme of change.” Mr. Weber called himself “a bit of a hypocrite” on immigration issues, because he employs recent immigrants in his business. (All of them are in the country legally, he added.) But Mr. Weber said he appreciated Mr. Trump’s calls for a tighter policy at the border.

“There has been too much, too quick,” Mr. Weber said. “Consequently it’s slowing down our school systems, crowding our housing, depleting our resources for our hospitals.”

Mr. Trump will make his second Long Island stop of the campaign on Thursday in Patchogue, where he will speak at a fund-raiser for the Suffolk County Republican Party. The choice of location has drawn protests from immigration activists: The event will be held at a nightclub down the street from where Marcelo Lucero, an Ecuadorean immigrant, was fatally stabbed by a gang of teenagers eight years ago, a turning point in the island’s debate over immigration.