Still, Trump voters interviewed said they cared little if the president spouted off on Twitter because he was issuing the kind of executive actions many had long craved — freezing federal grant money for environmental research, banning foreign aid for groups that give abortion counseling and cutting off immigration from several Muslim-majority nations.

“Trump’s done more in five days than Obama did in eight years,” said Doug Cooperrider, 58, who works in construction repairing bridges and roads around central Ohio.

The bar at Boondocks, where Mr. Cooperrider dug into a B.L.T. sandwich on a sleety morning, sits about 1,900 miles from the Arizona deserts where sections of the multibillion-dollar border wall may rise. The Hispanic population is tiny in this overwhelmingly white county of 35,000, and it has grown only 0.3 percent in the past five years.

Still, people here said they felt as if immigration had undercut wages for construction workers in the area. One man said he was uneasy about the longstanding Somali community in Columbus, about an hour’s drive south. Several embraced Mr. Trump’s directives that limited new refugees, ordered up the border wall and cut off federal grant money to cities labeled sanctuaries for immigrants.

“I’m 100 percent behind the wall,” said Ms. Cottrell, the salon owner. “If he asked me to lay the first brick, I’d sign up. I’m tired of them being here illegally and cutthroating the rest of us.”

She and her husband, Andrew, a Navy veteran, said their views of government had been colored by years spent struggling to get a disability claim approved for him by the Department of Veterans Affairs. They were early and enthusiastic Trump supporters, and when they went on road trips this year, they gauged their candidate’s support by counting up his yard signs and Hillary Clinton’s. Mr. Cottrell, 34, said he supported aid to feed and shelter refugees — but he blanched at welcoming them here.