Such a congressional action would violate the Constitution in two different ways. In designating administration of the federal district allowed under Article I, Section 8 of the Constitution, the document provides: “The Congress shall have power … To exercise exclusive legislation in all cases whatsoever, over such District as may, by cession of particular states, and the acceptance of Congress, become the seat of the government of the United States.” This defines the District of Columbia, which was explicitly not one of the several states. Article I, Section 2 also defines representation in lower house of Congress: “Representatives…shall be apportioned among the several States.” Only states may send members to the House of Representatives.
The pseudo-constitutional "non-voting" representative which the District of Columbia has is a "delegate," and these non-constitutional officials have been elected by territories since the Southwest Territories elected James White in 1794, and soon after William Henry Harrison was elected from Northwest Territories in 1799. Today Puerto Rico, Guam, the Virgin Islands, and other territories have such delegates in Congress. This serves a useful function: delegates from places remote from Washington, like Samoa, can provide information and answer questions which members of Congress might have about the distant territory. Those who choose to live in the District of Columbia, on the other hand, have much more direct contact with members of Congress than people in the states of the union.
Presuming that a “delegate” is really a member of Congress creates serious constitutional problems. If the a territorial delegate is a member of the House of Representatives, then why does Puerto Rico have only one member, instead of the six members that it would have if it was a state? If Puerto Rico is entitled to be represented in the House of Representatives, then why is it not also entitled to be represented in the Senate?
The proposal to grant voting rights to the delegate from the District of Columbia in exchange for lifting regulations on gun ownership is constitutionally flawed for other reasons. The District of Columbia has legislative powers or home rule only because Congress has granted it that. Under the Constitution, governance of the federal district resides solely with Congress, unlike every other state or territory. Congress, under the Second Amendment, is explicitly prohibited from passing laws abridging the right to keep and bear arms. State legislatures have powers under the Constitution which are denied Congress, but the expansion of federal power has been so complete, and the abrogation of the rights of the states so profound, that politicians in Washington and the pundits that follow them can seriously talk about whether to violate the Constitution by granting voting rights to the District of Columbia in exchange for reducing unconstitutional limits on gun ownership in that federal district.
Photo: D.C. Delegate Eleanor Holmes Norton, left, speaks with Paola Barahona, of Prevention Works!, in Norton's office in the House Rayburn building in Washington in 2007: AP Images