Mt Whitney Zone Forums General Discussion Looking For A Backpacking Permits for Two

Yes, you can get a permit and hike Whitney, almost any day.

Look at box 6, No Fee Permit Options, in the "Wilderness Permit Options" link to the left. Also, Google "Unused Whitney Permits" to get an idea of how many are available.

Also, there is a huge amount of info in the Orientation Notes, too. Please learn about altitude sickness, so you are aware when you go.