There's no such thing as anchor babies. Ending birthright citizenship is a constitutionally dubious solution to a fake problem. Our leaders play the people for fools (and, it works).
A woman comes to the US illegally, and yet is supported by the US government (hence her coming to the US) with welfare and social services. She has a baby, and the baby is a citizen. The government deports her, and she takes her baby with her (else, she abandons her baby, and abandonment is a crime).
It's not illegal for a citizen to leave the country. Duh.
How about a bill to end welfare to illegal aliens? The US should adopt Mexico's immigration laws.