I think what conservatives want is a free-market type of healthcare, with lots of specialist offices competing for customers which would result in better (and possibly cheaper) care. The obvious problems with this is the people who can't afford anything.
They certainly claim to... while pointedly and insistently refusing to acknowledge that (most kinds of, at the absolute least) healthcare doesn't
work like a normal market, and that the signals it sends trend pretty strongly towards resulting in the exact opposite of cheaper or better, much less both, particularly outside of a relatively very small fraction of said market.
The obvious problem with it is a significantly larger one than the people that can't afford it -- a normal market can adjust to that without much difficulty, to one extent or another. It's that a free market setup is fundamentally
anti-optimal (or whatever the blazes is below suboptimal on the sliding scale of optimality) for the services the market in question deals with. When you apply a free market to health care, what you're going to get out of it is not cheaper, or better, or more available, but rather the opposite as consumers are more or less literally incapable of sending the signals that would inform the market to be any of those... because for a great deal of said services, trying to means you're dead, or crippled, or otherwise rapidly moving outside the market entirely, one way or another.
E: Though, all that said, regardless of whatever conservative intelligentsia and ideologues argue on the subject, we now have clear examples of what conservative politicians are trying to
do, and it damn sure ain't trying to break healthcare into a free market. Looks a good lot more like "give tax breaks to rich people, to hell with the rest of you."