Here's an example of a fantastic national healthcare system. Our neighbors to the north in Canada, and here's one from Britain.
I have a friend of mine in the military (a "fantastic" example of a government run healthcare system) that is having to wait two weeks just to get a general appointment at the local military clinic.
NHS systems only work marginally well for people with no medical issues. As soon as you have a problem, don't expect to get any help in a reasonable length of time.