Nonrefundable deposits due before decision dates from other Universities

So my deposit for Cornell is due before I am likely to hear from a number of universities. It is nonrefundable and I would rather not lose that money if I choose not to attend because of an acceptance from a University later in the month. Is it possible for me to call some of these schools and ask for an expedited decision? Does anyone have any experience with this?

Thanks a lot

You may have better luck asking Cornell for an extension.