Flight time from BOS-DCA is about 1:45. Presuming you need to arrive 45min prior to your scheduled DCA departure -- allowing time to deplane and get to your departure gate before boarding stops for a 5:00pm flight, you need a flight schedculed to depart BOS by 2:30pm. You also need to receive your new passport and get to BOS, which is 10-15min by car with no traffic, in time for your flight. If the gate closes 15min prior to departure and you add 15min to traverse the airport, clear security, and get to the gate,you have to get your passport by 1:45pm to make it. There is N room for delay in any of this.

If it were me I'd plan to leave DCA as late as possible on Tuesday or (preferably) sometime on Wednesday that allows me to stay over at BOS if necessary.