What will it take to end the shutdown? There isn’t much that can be compromised in this situation, given that we have two issues at stake – the Affordable Care Act (aka Obamacare) on one side and the continuing resolution plus the debt ceiling on the other. There’s just not a lot of give when you have this kind of asymmetry. So it’s almost certainly going to be one side that caves.
As said before, it’s hard to imagine the President and his supporters in the US Senate giving in, so let’s just call that a low probability event. It’s probably going to be a Republican give of some kind. And one is brewing in the form of a general revolt of “pragmatic Republicans” who understand how dangerous this game is.