We drive from mid-Michigan (Lansing area). There are times we take I-69 down through Indiana and time was take 23 to 75 down. We tend to leave early in the morning to avoid traffic, sometime around 3 or 4 am.
I agree with BridgetBordeaux, avoid Atlanta during the rush hours. We tend to get to Valdosta on the first day. The next day, leaving around 7 a.m. gets us to Disney World after the morning rush around 10:30 to 11 or so. 8 times out of 10, they have a room ready for us and we can check in a start our day. If no room is ready, we just get our tickets and proceed to whatever park our plan has us going to first.
It's really not a bad drive, but I relax as the drive progresses. If you don't like to drive, then it can be a problem. Don't forget a DVD player for the kids. The "are we there yet" can be delayed by a response of how many movies to go until the destination. A six hour drive left just sounds better when the response is "3 more movies to go."