I gotta go with private but I wouldn't recommend anything major at first beyond tax cuts for medical expenses, Medical Savings Accounts and a little deregulation of the insurance industry (the really stupid laws first). This is a hard thing to flip over to private because it's such a big program and so key to the average American's life. I think eventually we can show the success of the free market in health care to all but the most ignorant Democratic partisans, but it would take some time.
I used to think that was possible, but as I watch public expectations I now realize that health care will be as impossible to fully privatize as it would be to privatize all the local roads and police departments.
There has been a sea change in the past 50 years in this country and it has now caught up to us. The change is in the work place and it shows up in two ways. The first is that businesses started giving out health benefits to employees
and their families on a regular basis. Perception of health care 50 years ago was that it was just that, a benefit. But now the public views health care as a necessity. You can argue that it is possible to put the genie back in the bottle, but I see no way that society will return to a level of expectations that existed before I was born (I'm 46).
The second problem that causes much of the failure in the private delivery of health care insurance are related to the changing nature of the workforce. When health care was a benefit, families were dominated by single wage earners who often spent most if not their entire career with one firm. That allowed insurance companies to control their risk because they knew who they were dealing with - and for how long. Over the last 25 years this model of employment has completely changed. Single wage earning household are the minority, and the 80's began a tradition of moving up by switching firms.
The existing system of competing private insurers can no longer serve this nation. Individuals who do not fit the original model are not served, nor does the private sector want them - too much risk. The current system also costs our businesses too much, and reduces their competitiveness worldwide. A new model using state and local resources can free up business capital and provide the services that the private sector no longer will undertake.