It already IS a private right! Everything that is not delegated to the federal government by the Constitution IS a God-given right and is reserved to the states and people receptively (10th Amendment).
Quit trying to create a Soviet Stater where the state creates rights, the State then expands its power to enforce, and the State may take away at any time. America is exceptional becasue it acknowledges the beginning point in the affairs of man is the INDIVIDUAL's God-given (not man-given) unalienable rights.The Constitution is aimed at binding the federal government to ensure it stays within those LIMITED rights and powers DELEGATED by the Constitution via the states and the people.