Generally-speaking, I think Republicans see the market as a cure-all. But this is a religious perspective.
The market is often a good solution to a problem. For instance, if you are selling soda. It provides a means to establish a price at which supply and demand offer the optimal result. This isn't the same thing as saying everyone can afford to purchase the good or service. In principal, some potential purchasers get left behind because they cannot pay the minimum price. Some folks are stuck with non-fizzy drinks (which accidentally is probably fortunate).
So there are some problems that the market doesn't solve well unless you are willing to divide the world between people who are able to pay for a good or service and those who are not. Healthcare is one of these. People whose consciences are engaged cannot abide the idea that poor people will suffer because they cannot purchase healthcare services.
Instead, most societies think some level of healthcare is a public good to which everyone should have access rather than a market style of choice.
Most societies. But apparently not Republicans. They seem to set aside their compassion in favour of their market faith. This allows them simply to look away from the problems it causes. Even though it causes them by definition. Intrinsically, some folks can't afford healthcare services at the market price (see above for the reason why).
I think there are ways to involve the market in healthcare. But starting with the notion that markets always deliver the best results isn't helpful. The best way to think about these sorts of problems isn't to apply a dogmatic idea. It's to look for solutions which work and to worry not a whit about words like socialism or capitalism.