The problem in the US is that each of the parties wants to solve it in a different way, so neither has broad enough political support to easily pass, but both of them have strong opposition from a different constituency.

The Democrats keep proposing some kind of single payer system, but without addressing any of the causes of the existing high prices (because that would gore the ox of all those healthcare providers, who have a lot of political power), so in practice the result would be to move the absurdly high cost fully onto the taxpayer, but they can't get through a tax increase that high. There are also some aspects of the US heathcare system (certainly not the price) that people do like, and their proposals would tend to make those parts worse.

The Republicans are mostly content to do nothing, but their main proposal when they have one is to push things like price transparency and regulatory reform. Those proposals have a lot of potential, but they would come entirely out of the margins of the aforementioned healthcare providers, so they can't get any meaningful support from across the aisle or even within their own party. Which is why they're mostly content to do nothing.

It also doesn't help that most of the reform efforts have been attempts to do the first one, which doesn't reduce the cost, but consumes activism resources to promote a proposal that either doesn't work or doesn't pass.