I collect and post the unused permits about once a month.
You can get an idea of what to expect on any particular day of the week and month if you look at the prior years' numbers. Above, you can get the link for 2011, and in the 2011 page, you can go to the 2010, and so on back to about 2007.
If you check the recreation.gov site multiple times a day, often a few permits will show up available in the week ahead of the current date. Here are the permits for July 1. Click previous 2 weeks to see this month:
DAY USE of Mt. Whitney Zone Mt. Whitney Trail Overnight Permit