We absolutely do not recommend trying to cross the continent in three days by car. That is simply playing Russian Roulette not only with your own life but with the lives of everyone else that is unfortunate enough to share the road with you. There is a reason that professional long-haul truckers are limited by law to driving no more than 600 miles a day, and that reason is safety. That such laws were not written to include every driver does not mean that it is safer for you to drive such ludicrous distances in such little time. Do NOT be suckered in by statements from those who have made it that it is possible, those who tried and failed aren't around any more to tell you their side of the story. They are now nothing more than grim statistics.
It is also not true that having multiple drivers lets you make better time. Quite the opposite. Having extra weight in the car certainly won't enhance either your speed or your gas mileage. And having extra bladders means that your stops will be both more frequent and longer. It is also simply not true that you can get quality sleep while sitting in a moving car. You may doze off, but you will not awake rested and ready to devote the attention and acumen required to operate a two ton auto at highway speeds. And one person's attempt to get sleep robs the driver of a useful co-pilot/navigator as well as keeping them from using the radio for information, entertainment, and mental stimulation.
The suggestion that a cross-country drive can be undertaken cavalierly and with less than the minimal time resources required is worse than foolish. It borders on the criminal.
AZBuck