See, and this is the problem-all the information available suggests that those who are actually involved in the conflict overwhelmingly do not support the "all or nothing" approach.
Here's the solution to that problem. If they are asking for help, they don't get to dictate(or rather, they shouldn't be allowed to) what form that help takes. If they want our military, we should be controlling it. If they ask for food, they don't get to bitch if we send rice and beans instead of filet mignon. See where I'm going? Personally, I'd rather we fix the problems here in the US before playing world police.
I see that you're taking the position that this threat of destruction should be applied equally to both sides, but really...what is the necessity for that here?
Simple, really. If we say we'll nuke the next one to put a foot wrong, you can bet there'll be plots to stage an attack from the other side. If we say we'll destroy them both, they'll both be working very hard to quell the psychos in their ranks. Once we've established that, the way is open for talks about who gets what land, with us playing the part of Solomon.