3-6 hours seems pretty marginal to me, though I guess it depends on what you mean by taxi sightseeing. It varies on time of day/traffic, but I would budget 1 hour for the taxi ride from DC proper (like the National Mall area) to IAD and then you'd want to arrive at least 90 minutes prior since you are checking luggage so that 2.5 hours plus 15 minutes or so to taxi from DCA to DC -- that's almost 3 hours right there, without any sightseeing.

I seriously doubt you can check baggage like that -- DCA to IAD is like 26 miles and DCA is a small station for United. But maybe I'm wrong on that.