If we had single payer, every Tom, Dick, and Harry would be going to the doctor every time they got a sniffle and the bill would be Trillions.
Bullshit. I live in Denmark. I have free healthcare and I can go to the doctor as many times as I want without paying anything. But I can assure you that I only go when I feel sick.
And it is not at all my impression that other people go to the doctor every other day. Sure, there might be some people who are really sick and needs to see the doctor quite often, and even those that think they are sick and goes often, but they do actually have a "disease" called http://en.wikipedia.org/wiki/Hypochondriasis
Every civilized country has free healthcare and free education for its citizens.