Every year, thousands of people make a deal with their doctor: I'll pay you a fixed annual fee, whether or not I need your services, and in return you'll see me the day I call, remember who I am and what ails me, and give me your undivided attention. But this arrangement potentially poses a big threat to Medicare and to the new world of medical care envisioned under President Barack Obama's health overhaul. The spread of "concierge medicine," where doctors limit their practice to patients who pay a fee of about $1,500 a year, could drive a wedge among...