That's the US perspective. In the medically civilized world, I would not make that assumption. Some might prefer the Swiss system which to me is more private insurance focused than the British NHS, but I would assume that right and left both agree on the basic idea of universal health care in Europe. Maybe I'm wrong?
I had American politics in mind when I typed that example. Like you, it is also my understanding that political support for universal health care is much more common in Europe than in the US.