If you didn't get a Whitney Trail permit, here are your options.
1. Go to the ranger station (intersection of hwy 136 and 395, on the Badwater route) the day BEFORE you want to do Mt. Whitney. The unconfirmed permits become available at 11:00 A.M. Go a little early, because there's likely to be a line, and very few permits available. If you're running, send one of your crew. I'm not sure if he can actually get a permit FOR you, but he can get the permit in his own name, and put you on there as an alternate leader. That way, you can go, even if that crew person doesn't. (Anybody know if you can just get a permit for another person?)
2. If you can't get a Whitney Trail permit at all, you might consider doing the North Fork of Lone Pine Creek trail (Mountaineers' Route). You DO need a permit for dayhiking this (new rule for 2007). However, there is no quota, so the permits are easy to get. You just go to the ranger station and pick up the permit before you go.
If you'd like to go down the main Whitney trail after you summit, you can get a permit to do that, too. I called the ranger station this morning, just to check on this. They tell me that there is no quota for this, so all you have to do is ask for the permit. There's no limit on the number of these they will hand out. (This is true for 2007, but check again for following years. It's likely to change.)
An important note: PLEASE DO YOUR HOMEWORK if you plan to do the North Fork trail. Not every hiker/runner has the skills to do this trail safely. Also consider that you may no longer have the ability to do this trail safely after running 135 miles! Also, I'd recommend that you don't attempt this trail in the dark unless you know the route, or have somebody with you who does. A couple spots can be tricky for routefinding the first time. When you get onto Mt. Whitney itself (the Mountaineers' Route) there's a whole lot of big, loose rock. And there's likely still to be some ice, especially up in the notch.
John and I have done the North Fork/Mountaineers' Route twice. The first time, we witnessed another climber being hit by rockfall. We worked far into the night to lower the climber 1000 vertical feet with a rope to Iceberg Lake, where he could be evacuated by helicopter the next morning. He had four broken ribs, a pneumothorax (punctured lung), and a displaced trachea. He easily could have died. On our second ascent by this route, we were called upon to rescue a man who went very badly off route and ended up literally hanging by his fingertips in a steep gulley. He had been hanging there for about an hour, and was so exhausted he could not speak. (He was a fit ultra runner, by the way.) I was able to climb down and get a rope around him before he fell. Anyway, we're two for two, having to do rescues on this route. Keep that in mind. If you have trouble, there may not be someone there to help.
For a good description of the North Fork trail / Mountaineers' Route, see http://www.summitpost.org/route/155528/mountaineer-s.html
Please note that this website is a little out of date. It states that you don't need a permit, but that's not true anymore.