WASHINGTON—House Republicans released 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.

Republican lawmakers are calling for work requirements, stricter eligibility verification and some co-pays.

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.