National health insurance "works" in other countries for three reasons. First, the wealthy, powerful and sophisticated – those most skilled at articulating their complaints – find ways to maneuver to the front of the rationing lines. Second, those pushed to the end of the lines are generally unaware of medical technologies they are being denied. Third, there are no (or severely limited) contingency fees, no generally recognized right of due process and no cadre of lawyers willing to represent those who are discriminated against.
National health insurance "works" in other countries because those who could change the system are best served by it. If a member of the British Parliament, the CEO of a large British company or the head of a major British trade union had no greater access to renal dialysis than any other British citizen, the British NHS would not last a week.
"Don't push me around" is a distinctly American phrase. In the United States we have widespread access to information about modern medical technology, a legal system that protects the rights of those without political power or money, and a strong devotion to basic rights of due process. National health insurance, as it operates in other countries, simply would not survive in the U.S. cultural and legal system.