Here's an idea:
UA:$695 DCA-MEX rt in First 6934PQM (w/ 50% class-of-service PQM bonus)
Tue 29 Dec
UA5708 DCA-ORD 0600-0716
UA359 ORD-MEX 0820-1245
UA474 MEX-ORD 1500-1905
UA5716 ORD-DCA 2100-2349
Link:
http://goo.gl/flights/nPO1
Multiple dates and flight combinations possible. Depending on exactly how many miles you actually need, you could also fly thru IAH in one direction and save some time (for slightly under 6400PQM). Fare is also valid out of IAD.
Note: the blue "book with United" button on Google Flights seems to be broken. But you can manually search for the same flights on UA.com, it seems to show up just fine.
Good luck!