Coming during a deep recession, the $3.4 billion, 4.5-million-square-foot public works project is being hailed as a boon to the local economy. The development, on a hill overlooking the United States Capitol and the Washington Monument, represents the federal government’s first significant presence in the District of Columbia’s blighted neighborhoods east of the Anacostia River.

But the mammoth undertaking has also drawn sharp criticism from preservationists, who say it will be devastating to a certified national historic landmark, the now-shuttered St. Elizabeths Hospital, a pioneering mental institution. Its residents over the years have included the poet and fascist propagandist Ezra Pound after World War II and, more recently, John Hinckley, who shot President Ronald Reagan in 1981...