Some legislators in Arizona are considering legislation to deny citizenship to so-called "anchor babies" born to parents who are undocumented. This would violate the 14th amendment to the Constitution, passed shortly after the Civil War, which reaffirmed that anyone born in the U.S., with a very few exceptions, is a citizen regardless of the immigration status of their parents. 

"Arizona targets "anchor baby" citizenship

From the Immmigration Policy Center's Immigration Impact: Reframing the Birthright Citizenship Debate with Facts by Seth Hoy

Defending the Fourteenth Amendment from the Immigration Policy Center

Made in America: Myths and facts about birthright citizenship a report from the Immigration Policy Center. Read a short summary of the report.