Yes, the ER, unfortunately, is always the priciest place to go. You need to phone them and try to work out some sort of payment plan, no matter how small amount a month it is. Frankly, you probably have the upper hand. There is nothing stopping you from saying you don't live in the US and IMPLY you could just walk away. So you can probably negotiate a really reasonable plan.
That said, if you DO choose to walk away, this could bite either your wife or her parents in the butt. They WILL send collections to whatever address you provided and they will try to find any phone number they can. I don't know about the legal ramifications, but your wife *might* be liable which, if she ever returns to the US, could end up being a real problem.
As someone with a great deal of debt myself, I can sympathize with you. But I can tell you from personal experience, it's really embarassing to have debt collectors phoning your parents or your inlaws.
If nothing else, you need to phone them.
Oh, BTW, an ER visit alone can cost $700. That's not including any tests or medications (i.e. you were obviously on some sort of IV drip). So, honestly, $3000 doesn't surprise me at all.