"The Second Amendment declares that it shall not be infringed, but this, as has been seen, means no more than that it shall not be infringed by Congress." -- US Supreme Court, U.S. v. Cruikshank, 92 U.S. 542 (1875), Presser v. State of Illinois, 116 U.S. 252 (1886)
Using this argument, a state or city so inclined could prohibit freedom of religion, freedom of speech, impose cruel and unusual punishments, etc etc. It's true that the Amendments in the Bill of Rights don't contain the phrase "the United States or any state" as do the more recently passed Amendments, but to put that forth as a serious argument is little more than sophistry and word games.