AUGUSTA — The House’s top Democrat on Wednesday morning presented what he called a “compromise” bill to expand Medicaid in the state to roughly 70,000 of the poorest Mainers.

It’s the first glimpse at what Democrats, who hold a majority in the Legislature, hope will be a bill that can gain enough Republican support to override a near-certain veto from Gov. Paul LePage.

The bill, LD 1578, is sponsored by House Speaker Mark Eves, D-North Berwick. It would accept federal money to expand the state’s Medicaid program, MaineCare, to all individuals with incomes under 138 percent of the federal poverty rate. The federal government would pay the full cost of expansion for three years before slowly ratcheting down to 90 percent federal funding thereafter.

Those three years set the stage for the main compromise presented in Eves’ bill: A sunset provision.

Opponents of expansion have questioned whether the state would realize the dramatic savings and benefits Democrats promise. Eves said that by sunsetting the expansion after federal funding drops from 100 percent, a future Legislature would have a chance to assess the pros and cons of expansion.

“After three years, prior to the decline in federal funding going to 90 percent, the Legislature would have to take a proactive step, and the good news is we’d have the experience of those three years to help make that decision,” Eves said.

Other elements of Eves’ proposed compromise include:

— An opt-out provision that would allow the state to cancel expansion efforts if the federal government reneges on its commitment to pay. Republicans, including LePage, have been skeptical about Washington’s promise to pay in the wake of federal sequestration and shutdown.

— A provision to require new MaineCare enrollees to make co-payments.

— The creation of a “MaineCare Stabilization Fund,” which would direct any savings from Medicaid expansion toward future costs.

The bill is sponsored by four Republicans, one Independent and five Democrats.