You can do it in 2 days if you don't plan on stopping early or doing any sight seeing. 3 days would be a much more relaxing trip.
Stay on the GA side until you get on I85, take it just into SC and then pick up Scenic Hwy 11 to Hwy 25 which will run you into NC and drop you on I26 just east of Hendersonville. You do want the interstate from 25 to Hendersonville as the backroads are extremely "fun" between the two.
In GA, go up 441 on the west side of the Okefenoke Swamp. You could stop and visit the swamp staying in the state park or travel up a bit father and stay at the state park just east of Douglas, GA. Then stay east of Athens hugging the lakes along the SC/GA state line.
