Can I find a last minute Labor Day camp site?

I have never camped on labor day, but decided I want to go next weekend. How full are campgrounds typically on Labor day? I don't have a reservation, so what are my chances for finding a spot at a State Park or COE within 2 hours of Tulsa?

Do any of you have advice for what I need to do to make next weekend an enjoyable camping experience? I am looking at Friday afternoon arrival and Monday afternoon departure. I still work full time, so I don't have much vacation time to pad either end of the weekend. It would be me, my wife, and the two dogs. I mainly want to stay in camp, walk the dogs, sit back and relax and do a little grilling.

Thanks in advance.