SaraD, if you really want to hike Whitney, you can go and pick up a walk-in permit if you understand the process. There are always a number of no-shows, and their permits are made available at 2 PM the day before the hike (for day hikes).
So if you are there at that time, you will most likely get a permit. You could then find a place to spend the night, and be able to start on the trail early next morning. You will find lots of others hiking the trail, so you won't be alone.
Good luck!
Here are the
unused permits numbers -- showing what is left at the end of the day.
