Guess what, everywhere else
that has implemented universal health care the local conservatives immediately tried to get rid of it. They succeeded nowhere
To take some specific examples in the English-speaking world, in Australia, the local conservatives did manage to repeal it the first time around. The second time around, they didn't get back into government for thirteen years until they promised to keep it, and they've never seriously tried repealing it since despite long periods in power. In the UK, even that hero of the right, Margaret Thatcher, left the NHS alone. The overwhelming evidence is that once universal health care systems are introduced, they are enormously popular.
So, yeah, drag this one out into a political fight to the death. It's unlikely, but possible, you'll knock it off. But if your lot continues with this crap for too long once it's in place, you will consign yourself to electoral irrelevance; even the ridiculous malapportionment and gerrymandering that goes on in the US won't be enough to save them.
In the medium term, I won't be terribly sad at that; while sensible health care reform will ensure that millions of your fellow citizens have healthier, longer lives, it doesn't affect me directly. But a couple of your party's other insanities, particularly its delusions on climate science, do. And if you do manage to consign yourself to complete electoral irrelevance for a few terms, the United States will be able to act effectively on climate change.