Simply not true.
It's been happening state by state for a decade now, driven by the unprincipled Romney Republicans at National Right to Life. It's also in the U.S. Code, put there by "pro-life" Republicans and signed into law by a Republican "pro-life" president, at the urging of the Romney Republicans at National Right to Life. Go look up the "Lacey Peterson" law. Like the legislation in question, it recognizes the personhood of the child, and then allows certain disfavored classes of said persons to be butchered by the abortionists. Immoral, unconstitutional.
Even the infamous Blackmun, in the majority Roe decision, admitted that if the child is a PERSON, they are "OF COURSE" protected by the explicit provisions of the U.S. Constitution. ALL of them.
-- Justice Harry A. Blackmun, Roe vs. Wade, 1973"The appellee and certain amici argue that the fetus is a 'person' within the language and meaning of the Fourteenth Amendment...If this suggestion of personhood is established, the appellant's case, of course, collapses, for the fetus' right to life would then be guaranteed specifically by the [Fourteenth] Amendment."
That's all well and good, but does even a legally-recognized PERSON have the unlimited right to the use of another person's body for as long as necessary? The Thirteenth Amendment is also part of the Constitution, remember, along with the Fourteenth.
I don't think the legal issues are as cut and dried as some people think they are. It won't do a lot of good to finally get the courts to recognize the personhood of the fetus if fetal homicide is then just considered another form of justifiable homicide.