What a silly question to ask:
Is a government-dominated health-care system unconstitutional? A strong case can be made for that proposition, based on the same "right to privacy" that underlies such landmark Supreme Court decisions as Roe v. Wade.
Whether government-domionated health care is installed or not (probably yes, unfortuantaely) will dpend on many factors. Constitutionality is not one of them. Half the stuff the government does today is unconstitutional, and nobody gives