About half of the campsites in Forest Service campgrounds are first-come-first served. So don't let the fact that you didn't plan ahead, and get a reservation, discourage you. Although a higher risk, if you get up early, you may even get a campsite on a holiday weekend.
But here's a tip for the spontaneous weekend camper:
Camp the weekend before and after a holiday weekend.
I'm not sayin' the campgrounds are empty. But, traditionally, they are not as packed as on the holidays or any other weekend during the summer months. In fact, if the campground allows a 2 week stay, you could find a first-come-first-served site the weekend before 4th of July and stay through the holiday weekend. When you are in a first-come-first-served campsite, you will not be kicked out for the holiday. Campsites must be occupied each day though. The Forest Service (and our) goal is for the campground to be enjoyed by people, not their camping equipment.
Here's another tip:
Camp during the last 2 weeks of August.
Summer campgrounds are full of families who have to get ready for school to start. If you want to take a longer summer camping trip, but don't want to be tied to a schedule, the last 2 weeks of August is your best bet for popping in to find an open campsite.
If the campground is full, ask the host what other campgrounds in the area have availability. Some hosts have the ability to communicate with the others and some do not; but it never hurts to ask.
Camp on weekdays instead of the weekend.
Very few campgrounds are full on every weekday; even in July. Sunday through Wednesday are the lighter-used days of the week. So, for the flex-hour worker, avoid the weekends altogether!