I wouldn't be surprised to see Peavy stay. His performance just doesn't meet the price. End of the day, he has pitched 80 games for the sox since 2010. Not exactly the history you'd like when dealing for an arm at the bounty the Sox are requesting. Factor in his age, his injury history and his contract (which to me isn't that bad but it is still more then a team may want) and you don't exactly "wow" potential buyers.
At the same time, even if you're asking for the moon and not likely to receive it, you still don't just dump him for bodies to put in the minors. There has to be something of value there because Jake can add value to the White Sox. It may be meaningless value this season. Who knows what is in store for next season and beyond, but I just don't think you dump him without something(s) of value.
If money is the hold-up, eat the money. If that is the difference between A and B prospects, you buy those guys.
I don't have the info in front of me but hopefully someone can reference it for us, and that would be where Peavy ranks as a type A or B guy. I'd imagine B, but you never know with that goofy scale.
Right now, I think Hahn may or may not be asking for too much (after all - it is rumors) and at least to me, he doesn't command the respect to be taken serious on things. So I think guys like Beane are willing to call his bluff and see what happens. They're willing to walk away from the deals, but we don't know if Hahn truly is yet. We'll know exactly what kind of GM we have once the deadline hits.