According to Judicial Watch's report on the subject, which was released in April of 2011:

[The] census Bureau data reveals that most U.S. families headed by illegal immigrants use taxpayer-funded welfare programs on behalf of their American-born anchor babies. Even before the recession, immigrant households with children used welfare programs at consistently higher rates than natives, according to the extensive census data collected and analyzed by a nonpartisan Washington D.C. group dedicated to researching legal and illegal immigration in the U.S.