Not to the concept, I think we need some kind of national program to address the health care crisis, but to the term. When you say "national health care" it immediately triggers the meme 'socialized medicine,' so successfully planted in the panicked masses by the GOP. Visions of waiting for years for hip replacements from 'government' doctors or whatever other alarmist anecdote is making the rounds, dance in their heads.
But of course, that is not what anyone is proposing. Nothing will substantially change but the manner in which you obtain coverage. I'm thinking the concept would be a whole lot easier to sell to the uninformed hordes if we started calling it "national health insurance" instead.