dont count on getting a site as a walk in. yes it is possible, but the past 2 years we have had to ask a generous person to stay a night in their parking spot and be in line at the kiosk by 630 or 7AM.
Be in line at 5:00 or 5:30 and your chances go up a lot. Also, if you don't get a spot in the morning, put your name on the waiting list and come back to check later. I have gotten that late call many times.
the fourth is on a thursday. Are you saying you plan to be there the 5th of July? If so, that would be problematic as people tend to make the 4th a long weekend. Thus they arrive either on weds or thursday and don't leave until sunday. Your chances go way down for a friday arrival.
Yep, that's a terrible time to arrive, due to the holiday. Instead of such torture, I would camp at Harden Flat(just before entry into park, free dispersed camping) Thursday night, do your climbing/hiking on Friday, then camp at free Warren Canyon (east of park), either the pullout, or walk into the canyon for sites with tables. You will meet lots of climbers there, and be close to the Mobil deli. Message me if you want directions.
I've stayed in the campground countless times-on the weekends, during the week and on holidays (even the 4th)-and I never needed a reservation. Just show up at 5-5:30, dress warm, bring a folding chair and a book (don't forget the coffee), plop yourself down and wait. It's worked every time. It's a drag to be up that early but think of all the traffic you'll avoid. I have'nt done it in a few years so maybe Spenchur's remarks are relevant. Good luck. It's worth it.