MIAMI — Dalia Carmeli, who drives a trolley in downtown Miami, voted for Donald J. Trump on Election Day. A week later, she stopped in to see the enrollment counselor who will help her sign up for another year of health insurance under the Affordable Care Act.

“I hope it still stays the same,” said Ms. Carmeli, 64, who has Crohn’s disease and relies on her insurance to cover frequent doctor’s appointments and an array of medications.

Mr. Trump and Republicans in Congress are vowing to repeal much or all of the health law, a target of their party’s contempt since the day it passed with only Democratic votes in 2010. If they succeed, they will set in motion an extraordinary dismantling of a major social program in the United States.

But for now, with open enrollment for 2017 underway, people are steadily signing up or renewing their coverage, and in conversations last week in South Florida, many refused to believe that a benefit they count on would actually be taken away.