Be prepared to sleep in the car. If you know anyone along the path, ask to sleep on their lawn or something. Start driving down probably a couple of days out. http://www.eclipse2017.org/2017/maps/whole-us.jpg
You probably won't get home Monday.
You probably won't get home Monday.
Could also check prices to fly to some other cities on the path in the map. Kansas City?
New York to/from SC is an 11 hour drive without stopping, and the eclipse in the afternoon, so definitely.