"Physicians and medical students from across the country are urging Congress...to lift the cap on the number of available residency slots." http://www.ama-assn.org/ama/pub/news/news/2013-02-03-urge-co...
"The BBA resident limits have imposed significant limitations on the ability of teaching hospitals and medical schools that sponsor and conduct graduate medical education programs to respond to the needs of the communities they serve." https://www.aamc.org/advocacy/gme/71178/gme_gme0012.html
I may be mistaken, but I don't think the federal government even has the power to restrict the number of residency slots.
[1] http://www.medpagetoday.com/PublicHealthPolicy/MedicalEducat...
http://www.advisory.com/daily-briefing/2012/08/30/why-reside...
A large majority of residencies are funded this way due to the very high cost of residency. As a result, many private institutions won't increase residency numbers on their own due to funding.
The main issue is the cost of residency is massive and is prohibitive for private money to fund anyone's residency.