I found a very thorough article via Arts and Letters Daily that answered my questions on the contributions versus costs of undocumented immigrants.  They contribute, according to this author, about 7 billion to social security that they never claim.  In addition, they pay enough property and sales tax to fund their children’s education.  Overall, the author claims, the cost to the public is a wash. However, native-born residents of border states do end up paying over $1000 a year to support newcomers.  Full article here:

Immigration Nation by Tamar Jacoby, in the Journal of Foreign Affairs.