It'll be close, I think, but probably doable without too much of a push.
We left, last time, a bit before noon, from NW CT (takes me an hour and 15 minutes to get to work in New Haven), and were into DC right around 6PM...I'd guess we weren't too far off Richmond at the 8 hour mark. I know we hit our hotel in North Carolina just before 11 PM. It's about 475 miles for us to Richmond. Depending on where you are in Southern CT, you could lop about 60 miles off that.
You're then probably looking at exit 77 or 57 in South Carolina for your day 2 stop. Those seem to have the best lodging selections. That should get you around 400 miles on day 2.
Then it should be an easy shot to WDW the 3rd day.....about 320-ish miles left.
One thing I wanted to clarify: I said we only make one stop, overnight in NC....what I meant was, we only do the drive in 2 legs, over 2 days. We make LOTS more stops because the kids bladders don't cooperate very well. I think we might have hit every rest stop in Jersey on the way down.....and about 1/2 of them on the way back.
This might help you out, too...we printed it, brought it with us, and used it a LOT.
http://www.wdwinfo.com/Transportation/Driving_to_Florida.htm
PS: Remember, the speed limit in much of the South is 70...you may find yourself making incredibly good time once you're south of DC.