The drumbeat for training additional doctors started a few years ago, amid predictions of soaring demand for health care in the U.S. Aging baby boomers alone are expected to fill many doctors' waiting rooms. And when the Affordable Care Act is fully implemented next year, millions more Americans will have new access to care.

Medical schools have increased their enrollments, and more schools are opening. But medical educators say a shortage of doctors is still likely unless the number of medical resident positions is increased...