First, look at last year's Unused Permits 2009
information. Sept 7 was Labor Day. While the Friday and Saturday following were pretty well used, from Sunday on, there were no less than 14 unused permits available.
And those numbers are from the END of the day. If you get there when the unused permits are first reassigned, there is a very high possibility that you will get one.
Read the Wilderness Permit Options information (link on the left), especially box 6 about how to pick up the unused permit.