I agree that there will not be time to do anything but drive and sleep if you try to make it coast to coast in 4 days. I have driven cross country many times and what you are planning is just not practical. Even a week would not allow you to really visit most sites along the way other than to spend 10 minutes taking a photo or two.
Most of the cross-country drive is drudgery from New York to New Mexico if you go via I-40. If you take a more northern route it is more scenic but longer and if you are attempting to take the trip in mid-summer you are not even going to want to get out of the car in most of Nevada and the Mojave Desert since it will be over 100 degrees. Don't get me wrong, I really like long drives and particularly crossing the west and southwest states.
But trying to drive that distance in such a short period of time is going to be a drag and allow you no chance to see anything other than flying by out the window.
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