I believe the general conservative thought regarding health care (extrapolated to anything social related) is three-fold.
• First, what's yours is yours, and you shouldn't have to share one sliver of it if you don't want to.
• Second, it's reportedly about "accountability". That is, if you can't afford health care, for whatever the reason, it's your own fault. You should have studied more, worked harder, saved more.
• Finally, by cutting people off from health care who aren't working, it will somehow motivate them to work harder, be more intelligent, competitive, etc. in order to get health care.
Coupled together, this will make the world a better place, and worked fine for many years in this country until the social programs in place changed things, and gave people a reason to be lazy, stupid. The bribery and collusion taking place, and warping of the laws and tax code preventing you from achieving any of this is a very minor point compared to what you could do on your own if you just put more effort into it.
Not that I agree with this, but it's the general conservative thinking across the board as I see it.