Zen's advice is a good place to start. Upper body strength is always good to have for a long ride.
My little piece of this will help with the distance. For the record, I'm jealous. I've wanted to ride cross-country since I was 15. When I was young, broke and didn't have a job, family or bills, I was too stupid to realize it was the perfect time to do it. Ah well, I'm not dead yet so it could still happen.
First off, don't think of your ride as 3,000 miles (or whatever your route is). That'll just mess with your head and make the whole thing seem bigger and scarier than it really is. What you are really doing is riding 50 or 60 miles a day for a couple of months. The best way to eat an elephant is one bite at a time.
Train to the point where you can ride 50 or 60 miles a couple of days a week and not be wiped out. Having a smooth cadence will make this easier.
Also, plan rest days on a regular basis. Every four days or so. And if you get up one morning and decide you just need a rest, pay up for your campsite for another day and spend a day doing bike maintenance, writing letters, read, eat or lay on the grass and look at the trees.
Realistically speaking, I'd be more concerned with ensuring you and your bike get along. Can you sit in the saddle for several hours a day without your butt going on strike? Are there any little quirks to your bike that bug you a little? Sort them out now because they will drive you looney after several hours a day.
re-cur-sion ri'-ker-shen n: see recursion