78 will probably be fine.
We used to go from San Diego to Phoenix in, hmmm, about 6-7 hrs I think when we lived in San Diego. I honestly don't remember the route we took. I think we went through Anza-Borrego if that helps. But I probably didn't like any of the routes since I don't like the desert, lol. I'm sure 3 days would be fine. Make sure you map out your overnight stops.
If I were you, I'd get a case of water to take, just in case you get stuck in the middle of nowhere...people have died (I remember a report last summer) from not having enough water with them when their car broke down.
Don't forget sunglasses and sunscreen!

And never wait 'til the last minute to fill the gas tank!