Its possible but you won't see any of the wonders of Route 66. Its 1000mi on the I-40, a bit further on R66 you will be amazed how long it takes to drive when stopping all the time.
Suggest you tackle a smaller section and do it well, get EZ66 Guidebook it will help you plan your trip.
June 15th to July 13th 2016
Did the whole thing, Chicago to Santa Monica
I agree with my friend thepengy. It's to much for three days. You won't have time to stop, and enjoy things along the way. Maybe the 500 miles from Joplin, MO to Amarillo, TX would be better. Most everyone agrees that 150 - 200 miles a day on Route 66 are the realistic numbers to make the trip more enjoyable, and less stressful.
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