Back in my BA days I wrote a research paper on the burning of Washington during the War of 1812. I don't have a comprehensive response for this but the answer is kinda.

After the invasion and burning of the capital in the War of 1812 once Congress reconvened there were some bills introduced to move the capital from D.C. If you look at the Congressional record in late August 1814 you can see some of these debates. But pretty quickly they died out and went no where. There were also some constitutional amendments introduced as well on authorizing Congress to fund internal improvements but overall everyone pretty quickly went back to "normal" and focused on rebuilding the city.

How hard it would be isn't an historical question but rather speculative. No one has the definitive answer to that because it wasn't done.