One problem with our system is that yes the price of surgeries, procedures, etc. are very expensive, but it's mainly because hospitals know that the government will foot the bill so they can charge a lot more. I'm not sure about ambulances being weird about payment like that, but no hospital in the U.S. will refuse a person in need, and if the person has no insurance the bill will get passed on to other taxpayers. The root problem isn't that people here are too greedy to pay more taxes, we just know that medical providers charge way too much for services because they can, it's the same problem with our University system and student loans.
I don't know all the answers, but I don't care about the politics and what not, in the U.S. we cannot get universal health care without changing how the hospitals can charge medicare/medicaid whichever they do. I wish everyone could get every bit of health care they need, but I know that the systems others in this thread are talking about have some pretty bad shortcomings. Here in California it would be a nightmare to implement universal healthcare, other states could do it for sure, but I don't even want to think about that train wreck.