WASHINGTON—House Republicans are unveiling an ambitious fiscal plan on Tuesday to rewrite the tax code, revamp medical malpractice laws, change federal employees’ retirement benefits and partially repeal the Dodd-Frank financial regulations—all in one bill that wouldn’t require any votes from Democrats to pass.

The strategy, embedded in the House GOP fiscal 2018 budget, faces political and procedural obstacles, including many of the same ones that derailed the party’s health-care bill in the Senate. For instance, Republicans...