It's desegregation of the health care system.
Right now, folks who have a health plan via employment (a situation that is increasingly becoming rarer), or those who have been fortunate enough to not have a pre-existing condition, and have the means to pay for health insurance (or have the means to get health care as a full payer, etc.) are able to go their regular private practice, where only folks like themselves are able to get into the waiting room, and then if care would be needed in the hospital, in the semi-private hospital room, or even the surgery recovery or ICU/CCU room. (Why anyone in the ICU/CCU would care about who else would be in there is a mystery, but I bet this would bother some folks.)
After HCR, anyone would be able to go that same physician's office or hospital - rather then only being able to go to the community clinics (a health care version of the historically black college) and public hospitals. To paraphrase Nixonally, now the Teabaggers are going to have to sit next to them, and their physicians are going to be spending their time curing them as well. Oh the horror!
Just about the only Congressional districts in the Deep South that voted for HCR were black majority or near majority. Cao (an Asian), the only Republican who voted for it (well, at least the first time - but only didn't vote the second time because as an ex-Jesuit priest he is super anti-abortion), comes from the black majority district based in New Orleans (and the only reason he won was because his opponent was "Dollar Bill" Jefferson, who is now doing the time for his crime. Since there may only be about 20% of the whites in the Deep South who are uninsured, everyone else figures that although it might be a good thing, the resulting desegregation would be too much of an irritant.
As someone who used to have regular private insurance before going into business on my own, and then having cancer that made me "uninsurable" after my COBRA ended, I can vouch for the social change that a patient going into the public system would face. This is what the teabaggers fear.