It's a completely obtuse argument from the opponents. Those with a vested financial interest in the current status quo have been using fear tactics to scare people into thinking that they are going to be losing access to health care or that these reforms will make them unafordable in one respect or another.
The problem is, and you're absolutely correct here, is that if one takes the time to understand how other modern, industrialized, capitalist nations have reformed their health care systems and have substantially reduced costs and improved outcomes, then one has to put on their objective hat and consider, maybe we ought to implement these fundamental reforms to our system too?
The whole "socialism" fear tactic is a canard that drives me up a wall. Hell a good majority of our health care system is all ready publiclly owned or financed. There's a huge difference between government being involved in health care to assure that our system is stable, available and affordable to all and provided basic and life saving care versus government running ALL of our health care system, which is what a socialist system would truly be. We need government as a partner in our health care system to stabilize it, improve cost controls, assure access and improve outcomes. Only government has the resources necessary to solve problems as large as these. If the free market could do it, we wouldn't even be having this discussion.