I drive, every February, to Hilton Head (theres a DVC resort there).. Its about 18 hours from where I am in NY during the day, and 15 at night (7pm - 10am)...
More than that, and I don't think I'd be able to do it... We've talked about going to Florida by car, but I wouldn't be able to stomache it...
So, its up to you... Personally, I do the drive because I like it... So, its up to you.. If you don't mind long drives, go for it... But, nothing beats getting on a plane, taking a quick nap, and waking up to palm trees in balmy florida...
What I would suggest, though, is going all or nothing.. Don't stop at a hotel... That just adds on two days of travel, which means two days less at WDW.. If you're driving alone, it might be you're only option... But, if you're driving with another driver, take shifts... Get a few books on tape, and you're ready for the 20-something hour drive! If it were up to me, I'd drive through the night. Less traffic, and I enjoy car trips at night better... You'll end up driving during the day at some point, but I would suggest starting right after a 5pm diner (in order to miss rush hour), and only stop for gas and bathroom breaks, and a sit down breakfast to take a short break...
Good luck!
-Gregory