Nobody can predict that - the longer the event (storm, snow, etc.) has gone on, the less the likelihood of finding a room, is my guess. Add the Hilton ORD, Hilton reservations and HHonors phone numbers to your cel, and try making a booking as ssoon as you know you will need it (and remember there are other Hilton properties with shuttle service nearby.) I'd recommend asking if they have a "distressed traveler" rate available.

Another alternative is to make a fully refundable booking and cancel once you know you are safe (e.g. on the aircraft and they have told everyone to turn off electronics because you are departing.)

Finally, the CTA Blue Line can be your friend - you can take it from the O'Hare terminal, very close to the Hilton, iirc.