The standard argument for nationalized health care -- our system is too expensive and ineffective, and nationalized health care works well elsewhere -- seems to me, to be very weak. Too expect our government to create a Health Care System as well conceived and run as, say, Austria's supposedly is is like expecting our Government to handle a bailout of our financial sector with the thoughtfulness and discipline with which the Swedish government bailed out its.
On the other hand, I think there may be a more reasonable argument:
Most of those who support a free market health care system believe that some amount should be subsidized for those who cannot afford it. It is similar, in this aspect to food.
In theory, the amount of food purchased, or subsidized, by the government is very small in relation to the total amount of food purchased. The government action, then, does not serve to distort the price of food.
With health-care this may not be the case. It may be that the minimum amount of health-care that should be available to everyone is beyond the ordinary means of enough people that the government will inevitably be a price-maker. We currently spend about $7,000 per person a year on health care. Even discounting that number a bit, it is an awful burden on a family making $50,000 (even inflating that number a bit to account for employer provided health-care).
If that is the case, the choice is between something resembling the current hybrid system or a more uniform nationalized system.
It is not hard to argue from there that the hybrid system -- where incentives are so misaligned and acountability and transparency so minimal -- is such a disaster that a nationalized system is preferable.
On the other hand, the per person spending may be reducible to something more affordable.
For example, there is the argument that our current system drives medical innovation. This may be true, but I do not see why the American patient is obliged to fund innovation for the rest of the world. In theory, I like the idea of price protection laws along the lines of: To receive patent protection for a medication or medical device, you cannot sell it in the US for more then some baseline derived from the price you sell it in other developed countries.
More fundementally, to get at the natural price of health-care, you'd have to figure out what it would cost without, for example, the (market) distortions of medicare/medicaid, often heavy handed state regulations and with a more sensible system to handle malpractice. Which is all rather hard to do.