There should be no such thing as an "Anchor baby" - Only babies born to parents here legally (legal resident or citizen) for more then 12 continuous months, and without evidence of receiving public support or assistance.
Unfortunately, you can't just decide that and make it so. I didn't stay at a Holiday Inn last night, and I might be wrong on this but I don't think when the Constitution was written there was a concept of "legal" versus "illegal" immigration, green cards or resident alien status, so deciding the 'intent' of the framers on the 14th as written is really speculative (and 'strict constructionists' shouldn't do it). I've seen activist lawyers make some fairly creative arguments about the meaning of words, but I think to change the right of citizenship from 'born here' to 'born here of legal parents' will take a Constitutional Amendment.
You might get it... But that's what it would take.