Update 3/1/2016 Reagan National has a dedicated nursing mothers room in Terminal A. Moms can express breast milk by pumping or breastfeed here if they want more privacy. There are 3 comfortable nursing rooms in all throughout the airport. Room amenities include rocking chairs, electrical outlets, and baby changing tables.
Terminal A: one room located just prior to the TSA Security Checkpoint
Terminal B/C: two rooms located next to Touch of Color on National Hall
Traveling Mom Valerie at Reagan wrote: "There is now a lactation room in Terminal A (mostly Southwest Flights) just before security (not airside). This doesn't help for people flying on the other airlines, since Terminal A is a schlep from the other Terminal and it wouldn't be realistic to use it unless you are on a flight out of Terminal A."