The constitution does not need to be changed. A proper test case needs to find its way to the SCOTUS to determine the status of anchor babies.
If it is decided that they are American citizens (which I do not believe to be the case) then I believe the language in the 14th Amendment itself, in Section 5 gives Congress the power to decide:
“Section 5. The Congress shall have power to enforce, by appropriate legislation, the provisions of this article.”
We’ll probably have to wait until we have an anti-amnesty GOP president (the non-GWB version) in order to pass such a thing, however.
“Section 5. The Congress shall have power to enforce, by appropriate legislation, the provisions of this article.”
Problem is Congress is mostly the immigrant loving Dems.