To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings
This one is vague enough on what can be done with the district that a Supreme Court challenge is definitely necessary. The problematic phrase: "To exercise exclusive Legislation in all Cases whatsoever, over such District" would seemingly be a roadblock for any local authority to have jurisdiction over the Federal government's responsibility to exercise legislative authority over the district.
Of course, that Constitution thing never stopped a Democrat...
See the 23rd Amendment.