After President Trump and Republicans in Congress spent much of the year trying to repeal the health law and cut spending on Medicaid, a half-century-old entitlement program that covers one in five Americans, the pro-expansion side in Maine is hoping to benefit from energized public support for it.

Turnout may be the biggest challenge for the advocacy groups leading the effort. There are no national or statewide races here to drive people to the polls this year. And Mr. LePage’s stance on government safety net programs appeals to many voters in the state’s more rural regions. He derides Medicaid expansion as “pure welfare” that would burden the state’s taxpayers.

Senator Susan Collins of Maine, one of the few Republicans who firmly opposed the Obamacare repeal bills, is not taking a position on the ballot measure — she never does on referendums, according to her staff. But leaders of the campaign are hoping her outspoken support for Medicaid during the repeal battles will help.

About 80,000 additional Mainers would become eligible for the program if the ballot measure were to succeed, according to the nonpartisan Maine Office of Program and Fiscal Review, although those with income above the poverty line currently qualify for subsidized coverage through the Obamacare marketplace. In all, more than 2.5 million poor uninsured adults across the country would gain access to Medicaid if the holdout states expanded the program, joining about 11 million who have already signed up under the law.