It sounds like you are planning on trying to day hike. If that is the case, permits for Tuesday might be available at 10 AM on Monday. Those available will be from others picking up permits and dropping off a few due to their group size reducing. At 2 pm Monday, all the no-shows become available. Since it is not a weekend, you have a 90-95% chance of success. Here are the
unused permit numbers.As for camping, get up to Whitney Portal. There are walk-in spots available just below the trail head, and more farther down below the overflow parking lot. They are never all filled.
Here's a thread with that info:
Sleeping in your car at Whitney PortalIf you are instead wanting to backpack up the trail, you could get an overnight permit (if they're available) any time Monday, to start Monday. You could hike up to Lone Pine Lake, or on to Outpost Camp on Monday afternoon. Since you are making such a quick trip, read up on AMS and altitude issues in the Orientation Notes to the left.
Please report back how it works out!