I can't find study now from CIS but when I dug into it, it lumped citizen children of undocumented immigrants into "undocumented immigrant", and other studies classify them as native/citizen. It also looked at estimated education costs since schools are required to take all school age kids without regard to immigration status and many of big school systems don't have a breakdown of immigration status. CIS argument was: If parents are immigrants, shouldn't be contribute the kids cost to them regardless of kids status?
Looking at CBO numbers, CBO reports that recent immigration into United States is drain, in particular, at state and local level since that's generally budget that gets impacted the most by people. https://www.cbo.gov/publication/61464