Here are some actual numbers from the Pew Research Center.
In 2014 there were 11.3 million undocumented immigrants in the U.S. This number has remained stable for about the last five years, and is down from our peak at 2007.
Of these undocumented immigrants, 8.1 million were working in the U.S. (2012 stats).
About 2.2 million of them are children.
So, that means about 1 million are potentially "sponging" off the American system. (Unless you want to count education and healthcare provided to children as "sponging").
.