It would be much easier and cheaper to detonate a van full of Cobalt 60 in NYC financial district.
Only big problem would be getting it into the city.
Yes, the dirty bomb scenario is almost certain to shut down an entire city, and with enough of them placed correctly, could bring the federal government to its knees, at least for a while.
The problem for the terrorists, as you say, would be delivery. There are radiation detectors in every major American city now, and most certainly in Washington DC.