I'm home! Thanks to all for the travel vibes.
It was a long day, but I arrived at DCA only about 10 minutes later than originally scheduled since I was on a non-stop flight.
This is what happened. We boarded the flight to JFK at 2:15 for a 3:05 departure. I called my friend in DC and told him what was going on. He offered to check my flight status (for both flights ) on the Delta website. In a minute or so he said, "This is odd. It says your flight is cancelled." I told him that we were all on board and asked why they would do that if the flight had been cancelled. Well, we chatted for a few more minutes and sure enough, the gate agent got on the speaker and told us the flight had indeed been cancelled due to weather and traffic control problems in New York.
My friend found the number for Delta and I called while still on the plane. I was able to get a non-stop flight to Washington, leaving at 5:25. I had to go to the luggage area and after about an hour the luggage from the cancelled flight came out. Then I had to go to US Airways to check in there. Then back through security. I got a little somthing to eat. I went to the gate for my flight and the agent said that there were no flights allowed to DC and that the flight would be leaving at about 6:10. But shortly thereafter we were able to board and actually left at about 5:55.
I had broken my own rule--I always try and get a nonstop morning flight, but the fares were substantially higher for those flights at the time I made my reservation.