As I'm sure you are hearing this is really not enough time - BUT - many do it or some simbilance of a trip in the three-four week time frame - problem is they are just rushed - but IMHO it's better to have tried than to have not.
Couple of things - it takes three or four days of driving to just get to the west, so you may want to plan the trip to catch the Coach after it is at least into the Rockies so as to not use up your time, just getting out and back.
When our boys were in College we would fly them out to meet us in Vegas or Denver and they would start from there, it allowed them to not waste there time just motoring in the Coach.
Take a look at the two websites - work on an itinerary - then let us all try to help fill in the blanks.
BOL,