Potentially a seat in the appropriate award class will open up a day or two in advance, but if so, AA won't let you know. You will have to keep checking (you can use aa.com and just look for one-way awards on the domestic segment only, then call AA if you see availability) or use ExpertFlyer (pay service).

If that doesn't work, request revenue standby at check-in as noted above. Of course there is no guarantee that there will be a seat for you; AA could fill its seats with paying customers or choose to upgrade its frequent flyers instead of accommodating you.