U.S. medical schools are expanding to meet an expected need for more doctors due to the federal health law. With at least 12 new schools opening and existing ones growing, enrollment is on track to produce 5,000 more graduates a year by 2019.

But medical educators are cautioning that those efforts won't do anything to alleviate a doctor shortage unless the number of medical residency positions rises as well. The number of federally funded residencies has been frozen since 1997.

Residencies are the three to seven years of on-the-job training in the U.S. that medical-school graduates must complete before they can practice independently in this country. Medicare funds most of the residencies, paying $9.5 billion a year to subsidize 94,000 positions at teaching hospitals. Medicaid and other sources such as hospitals fund about 10,000 more.

Medicare-funded spots were frozen under the Balanced Budget Act of 1997, and numerous bills to lift the cap have stagnated in Congress amid budget-cutting concerns, including proposals to slash Medicare funding for doctor training.

On Thursday, Reps. Allyson Schwartz (D., Pa.) and Aaron Schock (R., Ill.) plan to reintroduce a bill seeking 15,000 more U.S.-funded residencies over the next five years, at a cost of about $1 billion a year—a measure likely to face an uphill climb. "This has to be part of the conversation," Ms. Schwartz said.