Thanks Steve C.
Willaby, You might find this useful and have fun!
http://www.fs.fed.us/r5/inyo/recreation/wild/howto.shtmlYou might get lucky if you go in the day before your hike if you want to get an early start the next day,
"When can I get walk-in permits? Walk-in permits are available starting at 11am on the day before your entry date. Reserved permits that have not been claimed by the deadline will be cancelled and made available to other parties."
"When is the deadline for picking up reserved permits? Mt. Whitney
day hike permits must be confirmed or picked up by noon on the day before the trip. This will allow other parties to receive canceled day hike space.
Overnight Mt. Whitney permits and reservations for all other trails must be picked up or confirmed by 10am on the trip entry date."
So for overnight permits, the reserved ones that aren't picked up become available sometime after 10AM on the date of entry.