We travelled from April thru November for 8 years and never made a single reservation. We did sometimes call ahead a couple of hours before our arrival. We were never turned away from a campground. We didn't always get full hook-ups but did always get a place to park. However, we did make sure to get somewhere and stay put for the holiday weekends.
They way we travelled a trip from Colorado to the east coast would have taken at least 3 weeks. Most folks drive from Nashville to the gulf coast in 8-9 hours. We usually take at least 3 days for the same trip.