I have a friend whom I have this argument with frequently, not about health care specifically but other socialized benefits (e.g. SNAP). He's even a leftist, but still thinks he shouldn't have to pay for people who "take advantage of the system" (e.g. spend their SNAP benefits on things he doesn't believe should qualify, or receive SNAP benefits while spending their 'real' money on things he considers non-essential).
The fact that there are corporations getting orders of magnitude more in handouts, or that we're spending an unreal amount of money on the military, or that there's unfathomable amounts of corruption in the government, and that those benefits are in actuality a tiny fraction of what his taxes go to, makes no difference. He doesn't want people at the bottom to get an ounce more than he believes they strictly need or deserve, and I cannot for the life of me understand that line of thought.