I'd guess, they just don't know what they mean by "conservative". Maybe so.. but then again, I'm not sure they would know what you mean by "government intervention" in health care either, would they?
The devil is in the details.. and in a sound-bite society, the details tend to get lost.
I'd rather the questions be couched in terms of freedom.. as in.. "do we control the government, or does the government control us?" "Should your health care decisions be made by a government employee, or by you and your doctor?"
I spend time in France and Germany... great folks, (yep, even the French are very friendly to me).. but their mindset is not what has traditionally been the American mindset..
Little example.. bakeries in Germany (at least where I go) may not open before 6 AM (I think that's the time).. the people there think a rule by the government that dictates when a bakery may open is perfectly fine.. Here in the US, we would think that was a severe intrusion into the rights of the business owner.
In an even stranger example.. I was staying with a colleague at his home in a small town.. we were asked not to flush the toilets after 9 PM.. it was against the regulations.. (I guess they didn't have employees at the waste water treatment plant.. I don't really know).. but my friend was completely accepting of that decision being made by the government..
I think Obama, and most around him fully embrace that model of European socialism.. where while the government doesn't actually own the bakery.. it does, in effect, run it. I don't think most Americans, liberal/conservative/
Republican/Democrat/Whatever embrace that worldview. At least, I certainly hope not.