If your focus is to get out west then I would put in the long driving days on the front end, leave by 9am and off the road around 6pm, something like that should get you out there in 3-4 days. Is your plan to go to the Grand Canyon first and then head north? Or the opposite route?. Mid may you may still run into snow in the higher elevations, the GC plateau is 6000 plus feet above sea level so the temps will reflect that. On a trip like that there are plenty of things to see and distractions to spend time at that could eat up more time than you realize. Plan your route carefully to maximize travel time between your objective places you want to spend the real time at. Like others have said, its a vacation, not a road race. Don't make it all driving and not spend the time in an area that you really want to explore. It is truly beautiful out there and worthy of time you can devote to it.
