As the national capital, Washington, D.C. always has carried special meaning—representing both the federal government and the United States as a whole. No matter how Americans might feel about the state of the nation at any given time, they typically respect and revere the city—visiting on vacations and school trips by the millions each year.

Many might be surprised to learn, therefore, that at one particularly precarious point in the city’s history during the War of 1812, Congress seriously debated …