We didn't have to pay TANF, WIC, food vouchers and Medicaid to any of the groups you mention.
History is great, but no more important than Economics.
The immigration problem needs to become a non-problem. Close the border, now, and establish a port of entry every fifty miles, where migrant workers could apply for work visas. People that are already here could apply by mail and should be given priority.
That way we can get a handle on exactly how many have and how many we need.
Let them work tax free and keep every penny of their earnings. The trade-off? Absolutely no benefits whatsoever other than emergency medical care....for which they will be financially liable.
Work visas could be good for three years with one extension. After that, they should have already applied for citizenship or can return home.
America is indeed addicted to the cheap labor these people provide, but right now the sitaution is out of control. We ned to manage it, not end it.
Times change