this. woozy what would you think about a system like France's? france's government (as i understand it) provides health care for everyone, but if you want to get faster or better coverage then you can buy private health insurance, and get a small tax break for doing so. however, there is a cap on the amount you can spend on your own health care before the government steps in again.
that way you can get the best coverage that you want, always knowing that the government will help you out in the long run. however the free market insurance companies still compete, ultimately lowering prices.
this is a gross simplification that i drew from reading about it in my political science class months ago, but i think i got the idea right