Welcome aboard the RoadTrip America Forum!

You don't say where in northern California you'll be starting from, but using San Francisco as a first approximation, it's about 2900 miles to NYC. To do this in the 4 days you have allowed is doable with multiple drivers (you do say "we". You will have to keep up a steady pace of 700-750 miles each day. But by all means, plan to set aside some time each day to get out of the car and stretch your legs. There will be precious little, if any, time for sight seeing. For more information on such endeavors, check out Judy's The Art of the Speed Run. And drive safe!

AZBuck