Under a 2009 federal statute, National Parks must follow the arms-carrying policies of their host state. The National Park Service regulation implementing this statute includes the following exemption to a general ban on weapons in National Parks. “(h) Notwithstanding any other provision in this Chapter, a person may possess, carry, and transport concealed, loaded, and operable firearms within a national park area in accordance with the laws of the state in which the national park area, or that portion thereof, is located, except as otherwise prohibited by applicable Federal law.”
36 C.F.R. § 2.4. Thus, it might arguably be lawful to carry a concealed handgun at the Jefferson Memorial, if you have a handgun carry permit from your home state (or if you are a D.C. resident with a registered handgun).