+ 1 to Pedal Wrench's reaction - yikes.
Apparel: you'll need some really, really comfortable cycling shorts - probably three or four pair, depending on whether you'll be stopping often to do laundry. You should also consider long-sleeved jerseys, because that's a lot of sun exposure, and they do make summer-weight, long-sleeved jerseys.
Get some good sports bras, too, and wicking socks, and if you're really going all the way and getting clipless shoes, you'll want to make sure they fit you really well. (I have Sidis and they're awesome.)
Get a good helmet, too. Giants are great bikes. Oh, and good sunglasses are a must - they should fit snug to your face and not block your vision when you turn to look backward to the left for cars and other bike traffic.
See if you can determine the cycling experience of the people you're leading. Beginners will have trouble with steep hills. (Even some intermediate people would have trouble with some of the inclines in the western US.)
Build a really good support team. You'll want reliable people following along by car or van with supplies, medical help, food, etc.
Get really, really good at changing flats.
You might contact one of the companies that already does national tours and tell them what you're doing. They may share some insight on what you have to look forward to here. Maybe this group you're with already has this kind of support in place, though.
Two months to prepare for a 4,000-mile bike trip? Ah, to be young again.
Good luck to you, and welcome to TE.
Roxy
Getting in touch with my inner try-athlete.