The Constitution gives Congress exclusive jurisdiction over the "District (not exceeding ten Miles square) as may, by Cession of particular States, and the acceptance of Congress, become the Seat of the Government of the United States." While (as I read it) this provision does not require Congress to set up any such district as our seat of government, most proposals for DC statehood suggest carving out a tiny rump remainder of federal land (consisting of the Capitol, the White House, and maybe a few other notable marks like the National Mall or the Kennedy Center) to serve as said seat of government. As someone born and raised in the DC area, I've always found it more than a little outrageous that only a few miles from my house there were hundreds of thousands of Americans without any voting representation in Congress (I feel the same way about Puerto Rico, the U.S. Virgin Islands, and our Pacific island possessions too -- I really don't think America should be in the business of permanently possessing territories without granting full voting rights to all the residents).
In the comments to this post about DC statehood, some folks raised the potential problem of the 23rd Amendment to DC statehood provisions, and I agree with the person who suggests that Congress is well within its authority to shrink the "district" to a tiny core, freeing up the part where people actually live to become a state like any other. But there seems to be a different problem posed by the 23rd Amendment: It guarantees "[t]he District constituting the seat of Government of the United States ... [a] number of electors of President and Vice President equal to the whole number of Senators and Representatives in Congress to which the District would be entitled if it were a State" (so long as this number does not exceed that of the least populous state). By its terms, the 23rd Amendment guarantees these electors to the "seat of government" no matter how few people live there -- presumably, even if there were none. In other words, the new state of DC would be entitled to its three electoral votes (as the 49th largest of the now 51 states), and then population-less federal seat of government -- a separate body from DC-the-state -- would also be entitled to its own three electoral votes by virtue of the 23rd Amendment. One can even imagine a situation where the borders are drawn a little imprecisely and there are few voters left inside the "seat of government" in charge of three electoral votes -- a true rotten borough.
Are there solutions to this (aside from a constitutional amendment)? The 23rd Amendment does guarantee the "seat of government" a minimum share of electoral votes, but it also says that these electors shall be appointed "in such manner as the Congress may direct: It does not say that Congress must link its appointment in any way to the will of the seat of government's residents (however many there are). Instead, Congress could, for example, just hand the votes to the winner of the national electoral vote, or to the winner of the majority of the electoral votes in the 51 states.
Still, I kind of like the possibility of seeing the Columbia Community Improvement District replicated on a national level.