The whole framing of the abortion debate in terms of when life does or does not begin, and thus using that criterion in determining its ethical status, is fundamentally ill-conceived. A better argument is just to say that, in some cases, it's morally acceptable to take the life of an innocent human being.
Well The Constitution would hold that if it is deemed a person it is entitled to certain protections that can't be taken away without due process. So as a pro life advocate this isn't ill conceived at all, its a very good way to get what you want. There's an argument to be made on whether we should be following a 200 year old document, but that will probably go over about as well around here as me arguing that we should scrap capitalism.