Cato's Michael Tanner warns that Democratic health care proposals "would radically increase government control over one seventh of the US economy, would increase taxes, destroy jobs, and slow economic growth, and most importantly would lead to worse health care for millions of Americans." A lot to chew over there. I see no particular reason to think these plans would destroy jobs or slow economic growth, but those would be good reasons to oppose a health care plan.
"Worse health care for millions of Americans," on the other hand, genuinely might be a price worth paying. After all, a proposal that have eight million Americans worse health care, improved health care for 120 million Americans, left 160 million Americans with about the same health care, and saved everyone some money would be a fantastic health care plan. One could also warn in ponderous tones that would lead to "worse health care for millions of Americans." It's a big country!
The "jobs" issue is one that I think doesn't get pursued enough. There seems to me to be decent evidence that labor market flexibility leads to employment growth. It also seems clear that America's health care system generates substantial labor market rigidities as people with medical histories need to maintain a seamless web of insured-ness in order to remain insurable. There economic costs here seem potentially quite large, but obviously you'd need some really smart people to take a look at it.