Probably nothing, unless there's some common part that fails and stops the car? Is your battery very old? We had an alternator go out once and the battery was 8 years old, so it was probably the cause.
I'd just have a look underneath to make sure nothing important is leaking, check the fluids up top, and go enjoy the trip!
Also schedule some time for detours along the way, we've driven to the west coast a couple times and my only regret was not having enough time to see more things.
You get it!
I understand that the car will be running consistently for three days, but it is a machine. It is designed to do that. I've always been of the mindset that if you're driving 5,000 miles in 3 days vs 3 months, whatever will have broken in those 5,000 miles will break. Now, should you be towing or constantly going through Colorado mountain passes, different story.
And yes to detours. It's the whole purpose of the trip. I could have easily flown, but, it's Spring. The country below the planes over head will be gorgeous.