[saalweachter]

I don't know the current (post-ACA) situation, but the short answer about the US's emergency care laws is "sometimes".

For instance, suppose you trip and fall, and in catching yourself, shatter your shoulder joint.

The emergency room would be obligated to keep that from killing you -- making sure the bone fragments weren't going to sever an artery or anything, stitching up open wounds and the like.

The emergency room would not be obligated to restore you to (as much as possible) functioning. If you need an expensive 20-hour surgery with a team of specialists to put all the pieces of your shoulder back together, well, that's too bad. Sure, your shoulder will heal into an immobile lump without treatment, but it won't kill you, so not actually an emergency.