Actually Oh4 , it is not true that people with national health care do not know how it is being paid for. In Australia we have free public health care, and subsidised care for many health related services. We know exactly how much we pay each year in taxes towards this. People are not ignorant of where their taxes go, they know that taxes pay for health care, education, roads, infrastructure etc, and we all use these services according to our needs, so we don't have a problem with paying tax.
An example of when the tax is not seen as fair was the stamp duty tax on new mortgages. This was a tax that was preventing young people from being able to purchase their homes. It was excessive, and served no purpose but to feed government coffers. The people voted for the political party that said that they would abolish this stamp duty tax, and the tax was abolished.
Another example: Our previous conservative government brought in draconian industrial relations legislation that severely restricted the rights of workers, and gave employers too much power. The people voted, and now we no longer have a conservative government, and this legislation has be overturned.
The Europeans, Australians, well in fact much of the rest of the world, are very politically aware. It is arrogant to assume that because these countries choose to have national health care for all citizens, that they are ignorant of how their system works. They know how its paid for, and they approve of it.