This is an issue where I become pretty right wing - anchor babies. I hope I don't become labeled an unsympathetic asshole by anybody, but...
If a person who comes here knowing good and well he could be caught at any time and sent back home decides to have a child (knowing that it would become a citizen), then gets caught and forced to be split from his child -- who is blame for all of that? He/she is. The illegal component of that family (the parents and others) should not be allowed to stay - PERIOD. If he/she wants to take their child (their responsibility, mind you) to the country of origin where he/she belongs, that person should be able to (and usually are, from what I know). That way the family is not seperated. The person can then go about coming here the right way and his child can still enjoy life in the US under legal means.
You see, for me the focal point of this subject may have the anchor children in the name, but the cause of this condition was
brought about through people here illegally. I didn't make the guy have that kid when he knows he would be put in a tough situation through implementation of the law. I don't feel it's my place as a citizen to have the Govt. raise spending/taxes to help provide for that child. Do we not hold the illegal responsible for his action? They are still the primary issue here. I say the anchor baby go back to the original country with his/her folks, as it is the responsibility of the parents first to provide for that child.
If the family knows of a legal means of adoption they can use to keep their child here, to go to school here, etc. - they should be able to. If the illegal family has a legal family here in the states, there should be a system of allowing that child to stay with them, under the consent of the parents. This way the parents at least have a choice of their child's future (as they are legally responsible for the kid until he/she is 18).
Trust me, contrary to what I've been accused of, I'm not as polarized on this as that spiel may make me out to be.

I'm very open to discussion on the topic, but this is one where I do see a line drawn and it being flagrantly crossed - not so much on me as a citizen, but on the side of the child, with the parents making a conscious choice on having a kid they know good and well would be put into jeopardy in a situation like this. It's downright shameful in some regards.