The Affordable Care Act should be repealed in August and replaced with a new system that lifts national consumer protections and gives control of health care to the states, according to a proposal by a conservative group released Tuesday.

The proposal risks irking centrist Republicans who want to focus on other subjects. Republican leaders have said they have no appetite for another push to repeal the ACA before the November midterm elections unless such a bill clearly has the votes to pass.

Republicans...