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.

It sets up a potential showdown with fiscal conservatives, who have pushed their colleagues to overhaul the program and want the final Republican tax package to cut as much money

New mandates proposed for megabill would likely force states to revamp how they finance their programs or cut benefits.