I think I'm missing something. Why will they call you in a panic?
Which is why they put out these silly "take it or leave it" offers. They're trying to pressure you into giving up that leverage. When you call their bluff, you'll find you have a really nice negotiating position.
There are exceptions of course. Failed company acquisitions for instance generally don't leave you a ton of negotiating room (although even then it's not zero).
So in short they're going to call in a panic because they need you much more than you need them.