Depending on how early you get started and how late you drive the first day, about a day and a half.
Getting on the road in Suffern about 6:30/7:00 we stop for a quick breakfast, usually catch lunch around Virginia and can make it to about 30 miles short of the Georgia border by about 7:00 that evening. Getting on the road by 7:00 the next morning would put you at WDW around noon.
Last year, we left after I worked a midnight shift and got started a little later and my wife did most of the driving so we stopped ealier in Lumberton, NC. From there, starting a bit later than usual, we got to WDW by 3:00.
Hope that helps.