I have never been shut out getting a permit for Whitney. You do have to keep your options open though. When we went up the MR there were no day hike permits available. We simply got overnights instead and got a "late start". We didn't screw anyone out of an overnight because we had to draw in the daily lottery for spots and my son drew the worst number. So if we didn't use them, they weren't getting used.
When you do this you can choose an overnight starting that day (the easiest to get) or an overnight starting the next day. (if you had to take an over night for the next day you might be screwing someone out of one. And instead of starting LATE you're coming home EARLY) For the MR trip we took an overnight starting that day. When asked where we planned to spend the night we told the nice ranger - near the trail head. The parking lot behind the store is near the TH IMHO.
Using these methods I have always gotten a permit when I needed it. I didn't even bother with the lottery this year. My lucky streak will continue or I'll use another trail head. The permit hassle is really over rated IMHO..................................................DUG