I simply dont think its feasible from a runway length perspective. MTOW on 787 is 228 tons - of which 100 tons is fuel. Even if you loaded 50% fuel but had a full passenger load, you're at 178 tons or 356,000 pounds. The numbers I see put a 787 at least 6000 feet of runway at flaps 15. Add some heat, and its going to get very close to DCA's limit on length (7169 feet).

I can think of three other problems: #1 DCA's gates are not designed for widebody aircraft. With a 787 you would lose two gates for 787 ops (the gate for the 787 and an adjacent gate). #2 I dont think DCA is set to use LD4 containers which are used on 787s. #3 I think it would be a tough call to maneuver a 787 around DCA's taxiways.