Originally Posted by
m_yates
Moderately priced bikes in that class include the Fuji Touring, Novara Randonee, Surly Long Haul Trucker, and Windsor Tourist.
You could do it on your existing bike if you are comfortable on it. Personally I would want drop bars on any tour that long, but people have done it on flat barred MTBs. If you want a dedicated touring bike, the choices recommended above are all reasonably priced alternatives that have a proven track record of successful cross country tours.