We have done the drive twice (we live in Bristow, near Manassas).
The first time we drove straight through. It took us about 13 hours - but about 2 of those were due to an accident that closed part of 95 in N.Carolina. They routed traffic around some back country roads and it really slowed us down. By the time we got to WDW, we were exhausted (and REALLY had to pee!!). We were so tired, we felt like we were still in a moving car. The 2 of us switched off every 2 - 3 hours, but it was still very exhausting.
The 2nd trip, we decided to stop overnight in Santee, S. Carolina. We left around 5:30pm on a Friday night and made it to Santee around 1am. We stayed at the Hampton Inn for $89. The next morning, we had only a 5-6 hour drive to WDW. We were much happier with the stopover. We arrived feeling fairly fresh and ready to get started.
If you can't spare the time for a stopover, I recommend flying. The long drive really packs a punch to your energy.