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.

House Republicans aim to impose work requirements, toughen eligibility checks and slash provider taxes to deeply cut Medicaid spending.

House Republicans are proposing work requirements for Medicaid and are planning to limit states’ use of the lucrative provider tax, which some consider a loophole that allows states to increase federal spending on the program.