Actually a few 300+ pound people have done it. They simply start out doing what they can do. Sometimes it's only 3 or 4 miles per day at first. To finish in six months you only need to average 12 per day and most people are doing around 20 or more by the time they hit Virginia (not as hard as it sounds). 2 mph for 10 hours or 1.5 mph 13 hours.
Started at 300 lbs., now at 221, going for 150.