Though I haven't been there in four years I've spent an appreciable amount of time in metro DC (in-laws), walking around, going to museums, restaurants, Nats games, riding the Metro..etc. I don't think I ever saw anybody reading the Washington Times on any occasion...save for myself. I never saw a sold-out Washington Times box or an empty rack at a newsstand.
I think it's fairly obvious the paper is pretty heavily subsidized by fringe balls and wing nut groups.
But don't believe me...you live there. Observe for yourself. Let me know what you find out.