The federal government is most likely going to be funding most medical school education at state universities that have fewer conflicts and philosophical differences with the feds/policy. The goal with be to 1) increase the number of physicians/providers and 2) reduce the debt-load of physicians and thus allow them to work within the new lower-reimbursement medical model that is Obamacare. BYU is not going to relish being in bed with Washington DC when it comes to setting educational/research standards, curriculum and practical training (e.g. abortion) and will thus likely not qualify for fed funding, making tuition prohibitively expensive.
With a few exceptions, private medical education is going to be very challenged in the next 20 years IMO. The debt incurred will not be serviceable by the income stream that will be available in a socialized medicine system.
FWIW, BYU has never really focused its efforts on graduate education. The primary focus has been assuring undergraduate education for LDS students. This is the arena where most prepare and depart for mission service, meet potential spouses and marry--not in graduate school. Case-in-point: BYU has never opened a dental school, despite having huge demand (roughly 20% of US dentists are LDS) and arguably one of the most distinguished and capable dental educators right in their backyard available for a deanship.