I'm not sure you're considering all sides to the universal healthcare issues. The United States contributes the most money of any country by far toward medical research (close to 10x of what the UK contributes). The benefit derived from that is that countries like the UK get all the benefits of that expenditure without having to make that expenditure. So what you get is a lopsided benefit in non-US countries. This creates free riding.

So what happens is that as other countries free ride the United State's research, the US would have to not only foot hte bill for research and development (of which it is the biggest contribute in the world), but they would also have the bill for the fruits of that research - ie: the actual healthcare services and machines require to deliver those services. The United States doesn't get to pay a single bill and get great universal health care, it effectively pays twice for care while other countries pay once.