I've never had a problem getting a campsite in Whitney Portal, either hiker-in or family campground.
I'd recommend you be there by noon. The family campground is only 50% reservable. This seems to be around the time you have to get there to be successful in acquiring a site. The hiker-in the same way. However, I've walked off the trail at 4 PM and have snagged of these on a holiday weekend.
Bill