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.

In news from Washington, D.C., House Republicans have released a plan for sweeping cuts to Medicaid to help cover the cost of $4.5 trillion in tax breaks for the rich. The Congressional Budget Office projects the $880 billion in cuts would cause 8.

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