The proposal, which is to be considered this week by a key House panel, omits some of the furthest-reaching reductions to the health program but would leave millions without coverage or facing higher costs.

WASHINGTON—House Republicans are releasing their plan to cut Medicaid spending, with the program’s defenders in the GOP appearing to win the intraparty clash over how aggressively to change the system that provides health insurance to more than 70 million low-income and disabled people.

Republicans worried about losing their slim House majority next year are struggling with how to achieve Medicaid savings as even more Americans rely on the program.