Volunteer Ranger Bob R has posted a trip report here:

Whitney Trail, June 22 & 23

The details of the report are in the captions to the pictures, so please view them: 2011-06-22 Mt. Whitney via the trail

Heed the warnings about going up the snow slope without any hardware (ice axe and crampons): The slope can ice-up after the late afternoon shadow hits!

Here's his intro to the pictures:
I hiked to Trail Camp, spent the night. Next morning ascended 'the chute' to Trail Crest and went on to the summit. Got back to the Portal in time for a burger and beer.

The trail was pretty much snow-free up to Trailside Meadow, then constant snow from there on.

Temperatures were mild, and my 40 deg bag was fine. Water was available all the way to Trail Camp. Snow in 'the chute' was great for climbing and glissading during the mid-day hours. Icy at night, though.

It appeared that a party tried the switchbacks, but bailed after the cables. My guess is that 'the chute' will be the preferred route to Trail Crest for at least the next two weeks and maybe four.

Thank you for posting the report, Bob R!