I don't really know. I have to buy my tickets through the corporate (internal) travel-booking site. And prices are constantly fluctuating -- sometimes I'll go to book and find the lowest-price fare is a carrier I don't like, then I'll try the next day and it's my preferred!
And depending upon where you're going you've a choice of airports: IAD (Dulles), DCA (Reagan National), or BWI (Baltimore). BWI is usually a bit less expensive than the others -- and you can say "Hi" to NnBob as you fly over. Many sites you can enter airport code WAS for Washington D.C. area airports (i.e. "try all").
I think, but am not certain, that the lowest fares come somewhere around 3 weeks before departure. I tend to stop watching when I've booked a trip. *\;^)
Whoops... LoM knows a site through which you can shop all the wholesalers: http://travelzoo.com
And don't forget to check the wholesaler's fare against what you get from the airline direct.
We just ran a sample search on TravelZoo and it came up with Alaska, who apparently has a new non-stop to D.C. -- new routes tend to have the lowest fares.
Yuh. Be sure to say "Hi - Hi" before you say "Bye-Bye".