If you are going to go to DC, I would not go north to Chicago just to drive along the routing of Route 66. I'd head for St. Louis and take I-44/I-40. There are 2 ways to do that:

I-66/I-81/I-64
I-270/I-70/I-68/I-79/I-70

You can, of course, take I-81 all the way to I-40, bypassing STL altogether.

Follow I-40 to Barstow, then CA-58 to Bakersfield. From there, there are various choices to get to San Jose.