Illegal aliens currently in the US have used the "anchor baby" excuse for reasons they can't be deported.
Current citizenship laws are written so that when a child is born in the US, that child is an automatic US citizen, irregardless if both parents are in the US illegally, or here on work/tourist/education visas.
The citizenship laws should be changed so that before a child born within the United States is granted automatic citizenship, at least one parent must be a US citizen at the time of birth. If neither parent is a US citizen, the parents must claim citizenship for their child in one of the parents' nationalities.