“The truth is that Medicaid expansion will just give able-bodied adults free health care,” Mr. LePage said in a recent radio address. “We don’t mind helping people get health care, but it should not be free. ‘Free’ is very expensive to somebody.”

The pro-expansion side may have benefited from energized public support for government health programs in a year when President Trump and Republicans in Congress tried repeatedly to repeal the Affordable Care Act and cut spending on Medicaid, which covers one in five Americans. Senator Susan Collins of Maine, one of the few Republicans who firmly opposed the repeal efforts, has been an outspoken defender of Medicaid, although she did not take a position on the ballot question.

The health law gives states the option of allowing any citizen with income up to 138 percent of the poverty level — $16,642 for an individual, $24,600 for a family of four — to qualify for Medicaid, which states and the federal government both pitch in to pay for.

Under the Affordable Care Act, the federal government picked up the cost of new enrollees under Medicaid expansion for the first three years and will continue to pay at least 90 percent. States cover a significantly larger portion of the expenses for the rest of their Medicaid population.