I wouldn't say "easy" but it is do-able. I did almost the exact route above in reverse, but I stayed on the 40 all the way to where it hits the 15 in Barstow, CA.

I spent the first night in Little Rock, the second night in Albuquerque, and made it to LA in time for dinner on the third night.

It's a little easier to do it quickly when you are going westbound because you gain an hour every time you cross into a new time zone!