Americans reject public healthcare because your average American has incredibly narrow view of the world, and many people buy lies about public health care in other places.
They simply buy the lie that propagandist are paid to spread that public health care includes 'death panels' or insanely long ER waits, or that you can't pick your doctor (can you now?).
The larger problem is that the government deals with things that are sufficiently complicated that they require dedicated time to understanding them and Americans aren't willing to do that on a scale that impacts government policy.