This is a nice introduction to the argument for voucherizing medicare. It is a video with some helpful graphics on the size of Medicare in relation to other programs.
The most interesting contribution is the evidence for the effectiveness of markets in holding down healthcare costs. He cites two examples which are pretty well known (though he again accompanies them with very useful graphics): Lasik eye surgery and cosmetic surgery (elective). Since these are both entirely (or almost entirely) paid for by the consumer they have both actually gotten cheaper relative not just to other medical prices but also to inflation in the rest of the economy.
But the most interesting piece of evidence he introduces comes from abortion provision. It turns out that this has gotten cheaper over the years, too.
This is quite a remarkable piece of evidence. One of the first things that you hear when you point out to people that cosmetic surgery has gotten cheaper is that, "people don't really need it so they can afford to shop around." Of course, one can always use the economist's argument that people also need money and so do, in fact, find ways to shop around anyway, but the argument that cosmetic surgery and lasik might somehow be a special case and that the lessons learned from those fields might not apply to the rest of the medical field strikes most people as being sensible.
That is one of the reasons that the evidence of the price of abortions is such a handy thing for advocates of the free market in health care. Broadly speaking advocates for greater involvement in health care and the advocates of abortion rights tend to be on the same side. They can hardly say that abortions are not necessary. At least rhetorically they are committed to the idea that the typical seeker of an abortion is a poor mother facing serious health risks from carrying a pregnancy to term. The fact that these consumers are able to control health care costs more effectively than expert allocation should carry weight with people holding such views.
It also poses a question for conservatives (or at least those that are not libertarians and are against abortion and socialized provision of health care): if government provision of is so inefficient then wouldn't, in the long run, a more effective way of reducing abortions be to put government in charge of paying for them?
If the price of abortions had been going up along with the rest of our healthcare system then even with the government picking up 80% of the cost the out-of-pocket costs to the patient would be more than the entire cost of the procedure at present.