The cost of caring for patients who are near death accounts for a big piece of the government's medical spending. But a furor over a provision for government-paid counseling to plan for end-of-life care is steering lawmakers away from the issue.

Tucked inside a sweeping House bill to overhaul the health system is a provision that would require Medicare to pay physicians to counsel patients once every five years. During those sessions, doctors could discuss how patients can plan for such end-of-life decisions as setting up...