I assume you are trying to get standard awards. (The non-capacity-controlled awards for approx. double the miles are always available, as long as there is an empty seat.)

If you are flexible on dates and cities, I'd say you have a decent chance at getting something. Another big one is class-of-service flexibility. If you have enough miles and are willing to fly either F or Y to get where you want to go, you'll increase your chances somewhat.