This point is not as cut-and-dried as you seem to think. You'll find numerous arguments against that "fact." They pay into Social Security, but will never benefit from it.
Why wouldn't an American citizen benefit from it? We are talking about the kids that are born here to parents who are not legally resident. Those kids will benefit from their contributions to SS.
And demographically the U.S. actually needs more young citizens.
Valid point.
The Armed Forces at one point were eager to see immigration reform that would help recruiting. Food prices remain low partly due to immigration. To get to the "net" figure, you need to look at benefits, not just costs.
I am all for a system that allows properly vetted foreign nationals to join our military and get a fast track to citizenship.
Food prices are so low because agriculture depends on illegal immigration. If they had to pay their workers fairly, that would drive costs up somewhat.
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The birth of children to illegal immigrants costs society in many ways. One obvious way, right from the get go, is that Medicaid is paying for a lot of those births, under the Emergency Medicaid program. The rest of the cost of those births is just written off, which increases the cost to the rest of us. And those women, for the most part, didn't get prenatal care, which increases the risk of problems with the actual birth and the development of the child afterwards. That treatment is also paid by Medicaid.
Then there is the cost of providing various other benefits throughout the kids' life. That baby gets added to someone's household as a dependent. That household now gets more SNAP, TANF, EIC, etc. That kid gets free Medicaid and public school. The guardians get free child care.
I don't think there has been any study (that I can find, anyway) that quantifies that cost in a nice neat number. But just looking at the variety of programs involved it's certainly a significant number. A number that wouldn't exist if we simply changed the concept of birthright citizenship.
I totally agree that we need more young people in the US and I want to give opportunities to immigrants, especially from countries like Mexico, China, India, etc. But I want them to come over the right way, a way in which we can decide who comes over and in what circumstances so that we can have more control over the costs. The current system forces unknown immigrants with unquantifiable costs on us.