I'd certainly echo Judy's concerns about the pace you are looking at. 4 days would push your physical limits close to the breaking point, and 3 days would just flat out be unsafe, unless you've got 3 people driving and sleeping in a strict location.

Keep in mind that going a "Southern Route" via I-40 is just 25 miles shorter than going via I-70/Colorado, so you won't be getting any time savings by going this route.

If you do force yourself to do this trip in 4 days, even spaced stops would look something like Gallup, NM; OK City; Nashville; and finally DC. You'd need to plan to be on the road for 12+ hours each of your 4 days on the road.