The rough openings for my doors are a just barely too small
Generally the size specified is the "nominal" size. The actual size is a bit smaller. 

If you ordered from a big-box store, measure an in-stock 32" door of the same brand across the outside of the jamb to see if it will actually fit within your 31 3/4" opening. My bet is that it will. If there is no in-stock version, ask the sales person for the actual dimensions. BTW- don't forget to check for height, too, just to be on the safe side.

You do want a little bit of wiggle room between the door jamb and the framing so you can get the door level, plumb and shimmed, but, so long as the existing opening is square, you can get away with minimal wiggle room. 

If the opening's not square, you're going to have some work on your hands, or you're going to have to cancel this order and get smaller and/or custom doors.