Those families can be sent back to Mexico, but those children--when they grow up, are orphaned, etc.--are entitled to full American citizenship. They can come back; they can vote in state, local, and federal polls; and, if they choose, they can run for President.
I see what you're saying now, but this is not how it's working and you know it won't be done. Instead the illegals use the anchor babies as their basis to stay in the U.S. and that is a reward for their illegal actions. The way to eliminate this reward is to eliminate the automatic granting of citizenship of the children of people in this country illegally.
Section One of the 14th Amendment was written to clarify the citizenship status of the newly freed slaves. It was interpreted to give citizenship to the children of illegal aliens, and that interpretation can just as easily be reversed, or better yet, the law can clarified as suggested in post #3-that children born in this country to parents here illegally share the citizenship of their parents.