We should not separate a child and eir parents, but doesn't the anchor baby1 phenomenon call for a re-examination of how citizenship is granted? I recognize that the current scheme is mandated by the Constitution and is unlikely to change any time soon, so consider the following to be mostly a theoretical discussion.
On close examination it doesn't make much sense to grant automatic citizenship on the basis of where a person is born. A child born in El Paso automatically becomes a citizen, but a child born just across the border in Juarez doesn't. Assuming that US citizenship is a desirable thing, is the child in Juarez any less deserving of it? No; at the moment of birth there's nothing substantively different between the two. But only the child in El Paso gets citizenship. That, I think, highlights the fundamental irrationality of assigning citizenship based on country of birth: it reduces the concept of "citizen" to someone who has won a geographic lottery.
We obviously have, in our collective conscious, some sort of a standard for what makes a "good citizen". Witness the hoops that we make people jump through in order to become naturalized citizens. Why do we set the bar so high for people who were born outside of the country in comparison to those born inside? I imagine that there's an assumption that people born within the country will automatically grow up to be good citizens, but such an assumption is unwarranted.
As demonstrated by the opening paragraph above, the relative imbalance between requirements for natural and naturalized citizenship causes problems, though the imbalance itself can't be justified. This argues strongly in favor of rectifying the imbalance, either by making natural citizenship harder to obtain or making naturalized citizenship easier to obtain.
From a pragmatic standpoint making naturalized citizenship easier to obtain makes a lot of sense. If more people are legal then some of the problems associated with undocumented workers decrease: legal workers pay taxes into the system, feel free to participate in society, and are more difficult to exploit. On the other hand lowering the bar on citizenship does dilute the concept somewhat, though most people in the US being natural citizens its not apparent that it means much to begin with.
The other approach is to make it harder for people born in the US to get citizenship. Which raises the question of what do we do with people who are born here but who aren't citizens? Well, part of the solution is to decouple the right of residence from citizenship. We do this already for immigrants ("green card" and whatnot), so presumably there're no constitutional or human rights issues involved. But if you accept the premise that a sovereign nation has the right to control immigration then even right of residence shouldn't be automatic. We could solve the problem of anchor babies2 by predicating a child's right of residence on their parents'.
There's a lot to be said about this approach. I think that discussion of immigration policy in general could be improved if we decoupled right of residence from citizenship. Residency may, in the long run, lead to citizenship, but they are conceptually much different. One involves where you live, the other is something more nebulous along the lines of a compact of mutual co-operation/support with the rest society.
It's a complicated subject, and there's more I could say, but the hour is getting late and I have other things to be doing. The gist of things as I see them is that current policy makes citizenship distinctions the basis of geography, but such distinctions don't make sense when compared against the actual concept of citizenship.