As far as I know, for DC resident, they can't be sworn-in in VA. I have heard that the only exception is if they need their naturalization certificate for US govt orders or so. For example, if you are in the military but live in DC, you can be sworn-in in VA, provided there is an express need for your citizenship. For example, you need to undergo security clearance to have access to classified information for military purposes. It is possible other extenuating circumstance could bring about same day swearing-in.
You will have to wait in line to be sworn-in in DC. Hope that the presiding Judge is Judge Ricardo Urbina, a cool legal mind and a son of South American immigrants himself...
Is there a website I can find the Distrct Court oath dates/schedule for DC?