If they want it why do they keep voting in representatives who actively fight it the whole way?
This is kind of a pointless question, because the answer is complex and includes things like 'gerrymandering' and 'vote suppression', but it's still a fact that many elected representatives from both parties actively fight public health care.
It depends on how you phrase the question. "Do you want the US government to pay your health care bills" is a yes for most people. "Do you want to only have the choice of Veterans Affairs medical care" isn't quite as popular, and IMO that's what we'd end up with. (And considering the number of people who commit suicide by self-immolation to protest the VA's care... I really don't want that)
Yes, they do.