I was in the USA in late 2009 when all of this was extremely hot topic, there were heated discussion at my family Xmas gathering & then I got dragged into it because I live in Britain. I had to say that I liked the NHS very much but what Obama had achieved didn't look much like the NHS.
The impression is that it will be very slow, very bureaucratic, with only the most urgent medical cases being treated & everyone having to wait forever. Aunt1 had skin cancer which removed a big chunk from her nose; she had to around in public for months with a large bandage on nose to avoid embarrassment before she finally got repair plastic surgery (Medicare). With private care she would have treatment much sooner, & the perception is that with Obamacare she'd die before they got around to it. Aunt2 was literally ranting about how unfair that would have been on Aunt1. I don't know all of Aunt2's politics, but would have put her down as fairly "liberal" in most respects.
Obamacare is very bureaucratic; lotsa forms to fill in as part of getting your treatment. Limited facilities (hospitals) which may be far away & remove all illusion of choice in who treats you. US private health care packages generally aren't much better wrt forms & travel distances, but there's a perception that people have more choice with them, at least.
There's a strong perception that the government is useless at running most things so for God's sake don't let them take over medicine, too.
So it isn't all "I'm all right, Jack" bias. Ironically, half the reason Obamacare is somewhat rubbish (compared to NHS, at least) is because of the compromises Obama had to make to get it thru Congress at all (ironically).
Of course there were ridiculous & extremist but influential claims made then, too, from extremist media (Fox). Like how Stephen Hawking would be dead. You cannot begin to fathom how much my relatives HATE Fox TV. They boycott Simpsons stuff as a result, & I often wonder why that boycott hasn't spread to Britain.