This link shows 3 years in family medicine and pediatrics. Internal medicine, family medicine and pediatrics taken together already give you around 50% of all doctors.
http://www.faqs.org/faqs/medicine/education-faq/part2/section-4.html
44% is the most recent figure. It means that we can easily increase the number of doctors by 50%, possibly by 100%, if we get rid of the residency bottleneck.
Even that overall acceptance rate is almost unheard of. If you want to study engineering, there are schools that will accept you and put up only modest prerequisites (or, in case of University of Phoenix, no prerequisites at all) - as long as you pay money. If you want to study law, GPA 3.0 and a perfect LSAT score are likely to get you into a top-14 law school, such as Duke or Cornell. In medicine, GPA 3.0 and a perfect MCAT score mean 50/50 chance of not getting ANYWHERE, including Sticksville Medical College. I can't think of any field of study where the majority of applicants are unable to get into any school, even if they are willing to pay.
http://www.aamc.org/data/facts/applicantmatriculant/table24-mcatgpa-grid-3yrs-app-accpt.htm
And, of course, the acceptance rate would've been even lower if not for this massive debt load. It's all part of the AMA conspiracy to keep the number of doctors artificially low and their pay artificially high.