Will government healthcare be bound by Roe and Doe?

According to Roe v Wade, and even more by the more-important companion piece Doe v Bolton, the government can not place an undue burden on a woman's right to a medical procedure, just as long as her physician deems the procedure to be medically necessary. According to Doe v Bolton, if a doctor says a procedure is justified, the government can not fully stand in the way, and can only nibble around the outside.

Furthermore, a patient has a right, according to these cases, to receive medical care from a doctor in privacy and without the government knowing what is going on between the patient and doctor.

Interesting. Looks like either government rationing will undermine Roe v Wade, or Roe v Wade will undermine rationing. I'd bet on the latter.