You really don't need to do a massive amount of training to do a cross country ride. Some training rides with a touring load with either panniers or a trailer (whichever you are planning to use on your ride) to experiment with what is going to work best for you, are worth while.
Start your cross country tour steadily for the first two weeks, and the fitness will take care of itself.
The biggest hurdle you are likely to face will be of the mind. Especially if you are doing the ride solo, there will be times of self doubt and it's important to understand that even the most experienced cycle tourists face these doubts from time to time, and that they will not last more than a day or two.
As Pete said, it will be your determination that will get you through.
Have a good tour.