I've managed to drive from NY to CA in 2.5 days all by myself. This is my car in New York:

I've made seven cross-country trips. Each of them is different, yet the objective is always the same: getting to the destination in one piece. So you want to learn how to drive across the country fast? The better question is... can you?
Your age does matter a lot. The younger you are, the more likely you can plow through all day. Here's a chart on the maximum hours you realistic can drive based on age:
Ensuring comfort while driving is often overlooked, but having a comfortable seat for a long trip is CRITICAL. Spend time to position your seat where you can comfortably move your foot around with minimal effort. Discomfort will cut your driving hours a lot shorter.
Your overall health may be a significant factor in whether or not you can drive for an extended period. Alertness is a must. If you’re tired, it’s best to stop ASAP.
Driving during the day is also critical to aiding alertness. I usually start driving at dawn. Daylights prevent your body from winding down in response to the lower light levels. I don't push beyond 2 hours after dusk.
It’s obvious. Just for tips: Treat driving through a monsoon just like you would through a blizzard. Don’t forget about the winds too, even on clear sunny days. Bad weather will cut your distance traveled. With bad weather, it's not possible to drive across the country quickly, so don't beat yourself up and, more importantly, don’t endanger yourself.
Your body can’t handle staying in one position (e.g., sitting) for an extended period. Use your time at a gas station to walk around and get your blood circulating.
Especially true if you're not on the interstate. Some areas are so remote that you won't see the next gas pump for many miles. Plan ahead!
Don’t book hotels in advance. Use the HotelTonight app to book nearby hotels last minute. That way, you can go far as long as your body and weather allow.