In reality, Ms Abrams could not expand Medicaid “on Day 1,” as she likes to say — and likely not even during her first year in office. The state legislature, which has to agree to it, will almost certainly remain under Republican control. And the leadership will likely remain resistant even though a number of rank-and-file members, especially in rural areas whose hospitals are in jeopardy, could start voicing more support.

But Ms. Abrams, who until last year served as minority leader of the Georgia House of Representatives, insists the legislature will have no choice but to accept Medicaid expansion before long.

“Most of the hospital closures are in Republican districts and they know there has to be a solution,” she said in an interview. “I think there are real political consequences, as well as the moral and physical consequences that have been in place for so long. They can read polls as well as I can.”

Since 2014, the Affordable Care Act has allowed states to provide Medicaid coverage to adults with incomes up to 138 percent of the poverty level, or $16,642 for a single person. Currently, adults who aren’t elderly or disabled cannot qualify for Medicaid in Georgia unless they have small children and minute incomes — $7,480 a year for a family of three, for example. The state has more uninsured people — nearly 500,000, according to one estimate — who would become eligible for Medicaid under expansion than any but Texas and Florida.

Mr. Kemp, Georgia’s secretary of state, has echoed the outgoing governor, Nathan Deal, also a Republican, in dismissing Medicaid expansion as too expensive.

Ms Abrams puts the eventual cost to Georgia at nearly $300 million a year, though offset by savings in charity care and other areas; Republicans say it could be above $450 million. For some rural voters, Mr. Kemp’s message resonates more.