You may also want to check out some of the area campsites that offer sites on a first-come-first-serve basis. But be warned, they are filling up quickly.
While
ReserveAmerica is lousy for making reservations, I do find it useful for researching campsites and availabililty. Put in your criteria, and it will tell you everything in your area and what's actually available, plus amenities etc. It will identify national as well as state sites, plus private sites too.
I didn't get in a reservation in time for a site this weekend either, but my favorite campsite has nonreservable sites for walk-ups on a first-come-first-serve basis. I drove out from Houston yesterday after work and claimed my favorite spot, set up camp for the weekend, and will head back as soon as I'm off work today.
Good luck!