While there may be a case to be made for some manner of universal health insurance. For instance Friedrich Hayek, in the compellingly anti-socialist The Road to Serfdom wrote --
Nor is there any reason why the state should not assist individuals in providing for those common hazards of life against which, because of their uncertainty, few individuals can make adequate provision. Where, as in the case of sickness and accident, neither the desire to avoid such calamities nor the efforts to overcome their consequences are as a rule weakened by the provision of assistance, where, in short, we deal with genuinely insurable risks, the case for the state helping to organise a comprehensive system of social insurance is very strong. There are many points of detail where those wishing to preserve the competitive system and those wishing to supersede it by something different will disagree on the details of such schemes; and it is possible under the name of social insurance to introduce measures which tend to make competition more or less ineffective. But there is no incompatibility in principle between the state providing greater security in this way and the preservation of individual freedom.
-- the idea of doing it by expanding Medicare should be a non-starter even for the most dyed-in-the-wool socialist. Medicare is a complete horror to deal with. (I write from experience as the part-time office-manager for my wife's psychology practice). And that unlike some other government run health insurance programs. Tricare is very easy to work with, as is Oklahoma's version of Medicaid. (Kansas managed to foul up Medicaid by putting a free-market veneer on a government health-insurance program, but even the messed-up result isn't as cumbersome to deal with as Medicare.)