The question is what fraction of the population can afford it.
I am in support of socialized medicine, but most Americans like their healthcare when asked, and until that changes, the system won't change either.
There's also many, many types of universal healthcare (including the very crude version we currently have in the US), some of which have more support than others.
I would support a system like Japan, Switzerland, or the UK, but not one where private insurance is banned.