2 week is 14 days.
On an average, you (Might) travel 50 miles an hour (really! I'm not kidding).
6 hours a day driving time??? well, here's the math:
6 hours a day (times) 50 miles a day (times) 14 days equals 4200 miles.
So from Winston-Salem, NC to Los Angeles, CA (According to Bing Maps) is 2440.1 miles. Actual driving time: 36.15 hours. You could drive the distance round trip in 12 days averaging 50 mph. BUT ... you'll be exhausted and when you get to the points of interest, you won't be able to spend time there. Oh you can buzz by at 50 mph and say that you saw it. But what do you want ... to just see it, or to "experience" it. Get out, meet the local people, learn the local culture, customs, history. If you really want to make this an experience, you need more time, or a shorter distance.
If you could travel one day, park and visit the next day, and third day travel to the next spot, park the 4th day to explore again, you will find the trip much more enjoyable and meaningful.
So the question is, are go going for the drive, just so say you did it, or are you going so you can actually enjoy it and really get something out of it. If the second choice, you need more time!