Will this require a constitutional amendment??
Yes. It would require repealing the Fourteenth Amendment.
All you'd need to repeal in the amendment is this sentence of the Fourteenth Amendment: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside." Your amendment could read "Section 1: The clause 'All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside' is hereby repealed. Section 2: Citizenship to the United state and of the State wherein they reside is dependent on[insert]. Section 3: Congress will have the power to make laws pertaining to citizenship."
Not to say it'd ever happen, but you wouldn't need to kill the entire 14th Amendment.
I think it's a horrible idea.