We made the drive straight through this past spring, in about 22 hours each way with a few stops.
I think if you can switch off with your spouse or partner its not too bad. I took the overnight driving. I popped a caffeine pill and washed it down with a couple of Mountain Dews, and sang along to the cd player. Never felt sleepy.
We did this with 3 kids (5, 4 and 1) and they slept soundly through the night.
My wife's brother and sister-in-law made the same trip (we all live in upstate NY), and made it straight through also without incident.
I think it also depends on the length of your trip. We had to fit ours into a week's vacation (with the monday-friday workweek off), so doing the 22 hour trip gained us a day on each end. If you are going to be staying for two weeks, I would suggest an over night, since you won't be scrimping on your vacation time.
If doing the drive straight through, plan on a rest day when you arrive. We spent our first day by the pool and got to bed early and were ready to hit the parks the following day.
We're going to drive again next winter, this time in the motor home we bought this summer. This should make things easier for the non-driving spouse, as we'll be able to get some real sleep hopefully.