They could, yes, but assume for whatever reason you choose that they simply don't want to rebuild DC and decide to relocate the capital.
my only problem with that is that DC was built particularly to avoid giving 'bragging rights' to any existing city. So, if they decide to abandon DC completely (in which case, the land would be given back to Maryland, IIRC), I'd think they'd still want to carve out a chunk of land somewhere else and make it the new 'DC'... I'd think they'd still want it somewhere in the east, so the government people would still have easy access to NYC and Philadelphia and the rest (the east coast is still the economic and political heart of the nation). Faced with all that, I'd think they'd just rather build again in the existing DC...