House Republicans released a plan late on Sunday that would cause millions of poor Americans to lose Medicaid health coverage and millions more to pay higher fees when they go to the doctor, but that stopped short of an overhaul that would make the deepest cuts to the program.

The proposal, which is one piece of a sweeping bill to enact President Trump’s domestic agenda, including large tax cuts and increased military spending, omits the structural changes to Medicaid that ultraconservative Republicans have demanded. Instead, it bows to the wishes of a group of more moderate and politically vulnerable G.O.P. lawmakers whose seats could be at risk if they embraced deep Medicaid cuts.

It was published late Sunday night by the House Energy and Commerce Committee, which under the G.O.P. budget blueprint had to find $880 billion in savings over a decade. The panel is scheduled to meet on Tuesday afternoon to debate and refine the package.

Republicans have toiled to assemble a number of cuts large enough to meet that goal, which fiscal hawks have insisted upon, while appeasing lawmakers from districts where Medicaid enrollment is widespread.

Overall, the legislation would reduce federal spending by an estimated $912 billion over the decade and cause 8.6 million people to become uninsured, according to a partial analysis from the Congressional Budget Office that was circulated by Democrats on the committee. Most of those cuts —$715 billion — would come from changes to Medicaid and the Affordable Care Act.

The legislation’s remaining savings would come largely from changes in energy policy, including the repeal of two Biden-era regulations that affect car pollution and auto efficiency.