Since you have summers off, you should be able to pick up a mid-week permit almost any time in the summer! Check out the Unused Whitney Permits 2009
There are VERY few weekdays when there weren't overnight permits always available.
And those numbers are at the end of the day, after all is said and done. If you get there at 11 AM when the overnight no-shows are made available, you have a better chance. (It's 2 PM the day before for no-show day
And check the Wilderness Permit options (link is in the Feature Topics box to the left), especially box 6, for the walk-in permit information.