“Best vote of your life?” the president said, with a grin.

After Mr. Trump left, another resident, Kathy Rice, beamed as she drove her golf cart back toward her home. “The president,” she proclaimed to neighbors lingering around, “touched my dog.”

Mr. Trump had leaned over to pet the dog, a 3-year-old Chihuahua mix, as residents gathered to receive the hoagies, a mix of cheese and either turkey, roast beef or ham, bananas and bottled water. He complimented Ms. Rice on her black “Bikers for Trump” shirt. “The bikers love us!” Mr. Trump said, clapping her on the shoulder with a broad grin.

“They’re everything I thought they would be,” Ms. Rice said later, referring to the president and the first lady, Melania Trump.

Nancy Newkirk, a pencil wedged under her bandanna, stood outside her home smoking a cigarette. The 67-year-old, who works as a meat cutter in a grocery store, did not get to greet the president personally. But it meant a lot, she said, that Mr. Trump had come to their complex.

“He actually saw for his own eyes,” Ms. Newkirk said. “This is Naples Estates, and it’s trashed.”

Part of the roof of her mobile home had collapsed, weighed down by water still collecting in the storm’s aftermath. Water left brown stains on the ceiling that still remained. A musty smell clung to the home she and her husband, Dave, had lived in since 2009. But they still fared better than some of their neighbors, who lost their houses and possessions.

Hurricane Irma left the Florida Keys with the most damage, but it battered all of South Florida and left millions without power across the Southeast. Eight people died in a nursing home in Hollywood, Fla., and others were hospitalized after the storm knocked out air conditioning.