Did it 3 years ago from east coast to west coast (and back again) in a Grumman AA5B. Total time about 48hrs
Fully agree with YoungSW's warning regarding being fully aware of Density Altitudes - worst encountered was at Rawlings with D.Alt. of 10,000ft (but it did have a 7/8,000 ft runway!).
Other than that - it's relatively easy, far more so than in Europe
Routed Bridgeport (KBDR) - Clarion County (KAXQ) - Warsaw (KASW) - Grinnel (KGGI) - Broken Bow (90F) - Rawlings (KRWL) - Wendover (KENV) - Battle Mountain (KBAM) - McClellan(Sacrimento) (KMCC) then a quick flight to the actual coastal area (to tick the box!) and back to Bridgeport roughly the same route.
Suggest you get your up todate charts and Flight Guides (you'll need all three) via internet (I used Airnav's link - using the people you're hiring from as the postal address (with their agreement)).
Get yourself some old USA Sectionals to study before you go. It'll give you a heads up on their airspace and stuff. The Flight Guides give you lots of useful information in regards to the various aspects of operating over there.
You do have a USA license, yes?
If not you'd better start organising one, either on the back of your UK one or a stand alone edition - all of which will involve time and probably a bit of work!
Fly safely