Anchor babies may be American citizens but in many situations, and I'd wager the majority, their parents are not. This means that the children get the benefit of American taxpayer dollars such as education when there parents don't pay a cent. I don't mind that they're here, I mind that their parents aren't contributing via taxes like the rest of the legal US citizen.
Personally, I just wish they'd streamline the citizenship process so we could get taxes from the anchor baby parents. Changing the 14th amendment isn't the right answer, IMO.