Hi Charlie,
It sounds from the post like this is something you are doing soon and need help with quickly. I probably can't help much but I'll tell you my story.
A quick trip like this might be amazing and fun especially if you are a spontaneous couple and willing to just see what happens. I kind of did that on my first attempt at a tour. I took my hybrid bike with a small rear pannier and did a 1 week credit card tour. I only spent a couple weeks in planning and most of that planning was to guess how far I could ride each day making sure that I had a motel at every nights stop. After that trip I found out I needed to do a lot more research before I headed out cross country - mostly because I realized I could not afford a 3 month credit card tour. For me, I decided I needed a proper touring bike with lower gearing and I needed all the camping equipment and panniers, and racks. I researched this whole subject steadily for about 18 months. I bought a used touring bike In new condition off of Craigslist for $600, and then started purchasing each additional item on my list as I found them on sale or craigslist - probably about 1 major item per month before I left on my first cross country trip. About half of my research came right here on these forums both asking question and searching and reading old posts, the other half of my research came by google searching other bike touring sites and just reading and reading, and making list of questions and looking for answers.
So that said, what I did, after deciding I wanted a traditional steel frame touring bike was this: I went to a couple stores and found out what size bicycle I would likely need because I was going to try to find something used. I then made a list of the most often recommended touring bicycles, such as the Trek 520, Surly-LHT, Fuji Touring, REI randonee, etc, etc, I had about three more on my list then I started typing in these brand names in craigslist every other day for all of the regions in Northern California, until I found one in my size. Actually found several bikes for sale looked that like ancient things, and since I'm not a fix it myself person I kept looking but within a month I had a REI (Novara) touring bicycle that was purchased for a cross-country trip and then never used and I bought it for exactly 1/2 of what a new bike cost.
Anyway thats my story. If you are young and adventurous and can muscle your way through the mountains on a bicycle that doesn't have low gearing you will find it easier to get something to get by. --- just take off and have fun.