Last fall I did exactly what the OP is trying to do (LHR-ORD-DCA). I cleared customs fast at ORD. Domestic departures were running late and at my request they put me on the next flight to DCA which (though late) left sooner that my scheduled flight. I was on a deep-discount ticket.

Remember the previous advice about no checked bags; it is correct. However, you can check the bag on the international leg and then keep it when you go through customs if it is small enough to carry on.