New Columbia Admission Act - Sets forth procedures for admission into the United States of the state of New Columbia.

Requires the Mayor of the District of Columbia to: (1) submit to the eligible voters propositions for statehood and adoption of a State Constitution, and (2) issue a proclamation for the first elections to Congress of two Senators and one Representative of New Columbia. Requires the President, upon adoption of such propositions and certification of such elections, to issue a proclamation announcing the results and admitting New Columbia into the Union.

Provides for conversion of District government offices to state offices.

Provides that New Columbia shall consist of all territory of the District as of the enactment of this Act, excluding land within specified metes and bounds that shall remain the District of Columbia and that shall include the principal federal monuments, the White House, the Capitol Building, the Supreme Court Building, the federal executive, legislative, and judicial office buildings located adjacent to the Mall and the Capitol Building, and certain military property.

Prohibits New Columbia from imposing taxes on federal property except as provided by Congress.

Maintains the applicability to New Columbia of current District laws and continues pending judicial proceedings.

Maintains: (1) the District of Columbia as the seat of the federal government, and (2) the federal government's authority over military lands and specified other property.

Requires each state that is the last place an individual resided before residing in the District of Columbia to permit such individual to vote in federal elections by absentee ballot. Sets forth a rule for expedited consideration of a joint resolution proposing an amendment to the Constitution to repeal the 23rd amendment (which provides for the appointment of electors for President and Vice President for the District).