The first time I summited Mt. Whitney, our group did it in mid-June. As we reached Trail Camp, we caught the last people of the season glissading down the chute, and it was a rough go for them.
We did the switchbacks with microspikes and there were a few rough areas, especially around the cables. Altogether we had an easy go of it but as first timers who had attended seminars, trained, acclimated and brought all the proper gear, it was still a LOT of work.
My advice would be to go, be extremely cautious and proceed only as far as you can. There's no harm in getting to Trail Camp, seeing the chute up close and enjoying the scenery. It's a beautiful hike up to that point - one of the most picturesque places I've ever been - and in our experience, the real work began as soon as we left camp at midnight and headed for the switchbacks.
Photos don't convey just how incredibly massive the chute and the switchbacks are. It's something you can only understand by standing there and seeing it for yourself. No sense in getting stuck halfway up and realizing you're not prepared.
Talk to hikers coming off the trail and see what they have to say at the Whitney Portal store. Those are going to be the most accurate reports you'll get in terms of what the conditions are, but not much is likely to change over the course of just a few days. Take it slow and enjoy however much of it you're able to do!
