AUGUSTA — The debate over Medicaid expansion has dominated the 126th Legislature, and will continue to do so as the session winds down and lawmakers prepare to head back to their districts.

On Thursday night, the last scheduled day of session, House Speaker Mark Eves, D-North Berwick, plans to present a last-ditch effort based on a plan approved by Republicans in New Hampshire, ensuring lawmakers take one, final vote on his party’s top priority.

The plan would accept millions of federal dollars to expand Medicaid for one year to newly eligible poor Mainers as a “bridge” to a new system in which the state would use the federal money to fund subsidies for about 55,000 low-income childless adults. Another roughly 15,000 parents would remain on Medicaid, known here as MaineCare.

The childless adults would receive subsidies from the state to purchase private insurance through a new “Maine Marketplace Premium Assistance program,” which would be administered by the Department of Health and Human Services. If they are eligible for insurance through their employers, they would have to purchase it, and enrollees under the new system would be required to pay premiums and copays as authorized under federal laws.

In the Granite State, a GOP-controlled Senate and Democrat-controlled House approved a similar plan subsidize private insurance plans for roughly 50,000 New Hampshirites.

The plan will require a federal waiver, but state officials in New Hampshire are optimistic that President Barack Obama’s administration — keen to see state-funded health insurance expanded as envisioned by the landmark Affordable Care Act — will grant the waiver. A similar waiver has already been granted to New Hampshire

The plan has gained traction with Republicans in New Hampshire because it does not permanently expand the Medicaid rolls. Democrats there accepted the plan as a feasible workaround to Republican opposition to welfare expansion while still accepting millions of dollars every month from the federal government.

Eves is expected to push the plan in an amendment to a Medicaid expansion bill he submitted this winter. It will mark the third push for Medicaid expansion since January, though Eves said his plan is “dramatically different” from any plan the Legislature has seen before.

“New Hampshire has recently successfully passed a version of Medicaid expansion that puts the vast majority of people on the private health insurance exchange — something Arkansas has also been able to do,” Eves said Thursday. “Both states successfully negotiated an agreement while having a divided government. I have to believe, and hold out hope, that if New Hampshire can do this in a divided government, we can do it.”

Thursday marks the last regular day of the legislative session, and Eves’ spokeswoman, Jodi Quintero, said the Medicaid plan will be the last thing on the agenda before lawmakers leave Augusta.

Eves has been the most vocal proponent of Medicaid expansion since the 126th Legislature began in January 2013. The Democrat-controlled Legislature in Maine approved expansion twice last year, only to be thwarted by LePage’s veto. This year, lawmakers approved a compromise plan by two moderate Republican Senators — Roger Katz of Augusta and Tom Saviello of Wilton — which the governor also vetoed. Overriding the governor would require two-thirds support in the Legislature — a threshold impossible to reach without Republican support.

The overwhelming majority of GOP lawmakers have stuck with the governor, which has allowed each veto to stand.

Another expansion effort, by Senate Majority Leader Troy Jackson, D-Allagash, was enacted this week and faces a near-certain veto. Lepage is expected to veto any expansion effort that crosses his desk, but Quintero said Eves couldn’t be deterred by the governor.

“Speaker Eves will do anything to ensure that tens of thousands of Maine people have access to health care,” Quintero said Thursday. “We could not leave this session without making every last effort to ensure that this bill could pass without exhausting all potentials for this bill.”

It is unclear whether Eves’ plan will have any real traction with Republicans in the House or Senate, the vast majority of whom have so far resisted any and all efforts at expanding Medicaid.

Still, the amendment, like the Katz-Saviello plan before it, is designed with GOP concerns in mind: If the state is unable to obtain the necessary federal waiver by August 1, 2015, the “bridge” expansion of MaineCare will be repealed. It will also be repealed if federal fund drops below promised levels.

A provision of the Affordable Care Act, sometimes referred to as Obamacare, allows the states to expand Medicaid, known here as MaineCare, to every resident who makes less than 138 percent of the federal poverty level, or just under $16,000 per year for a childless, single adult.

The federal government will pay the full cost of expansion through the end of 2016. After that, its share of the cost will drop, incrementally, to 90 percent. Those are the funds that will be used to subsidized private plans in Arkansas and New Hampshire, and would be used under Eves’ plan in Maine.

Expansion was a linchpin in the federal health care overhaul, which envisioned state-funded health care for the poorest Americans and subsidized private health insurance plans, through new online exchanges, to anyone making between 138 percent and 400 percent of the federal poverty level. But the U.S. Supreme Court in 2012 struck down the provision of the law requiring Medicaid expansion, leaving the decision up to each state.