We have gotten a crib twice at SSR, once at BLT and once at VWL. Never have had a problem - requesting it on the reservation and then called when we got in the room. Of course that was always during non-peak times.
As a back up option, you might want to look at getting a portable air mattress like the ones they have at onestepahead.com. They are raised on the sides so they can't roll out. We used one of those one time at a hotel and always had it as a back up at the resorts in case.