The pre-1920 immigrant waves were almost all legal, checked closely for communicable diseases (at least after about 1890), and were expected to "root, hog, or die." All the caterwauling of the pro-immigration crowd and their dredging up ancient stories of the Know Nothings of the 1850s or the Ku Klux Klan of the 1920s cannot change this fact.
Ideally, public assistance should be left to the private sector, as was the case, even on the local and state level in most instances, until the Depression. However, illegals, who are often paid off the books and whose tax payments through sales and property taxes are relatively small, receive educational, health care, and other benefits far superior to what they would have had in their native lands. The corporate supporters of unlimited immigration receive the benefits of cheap labor. Only the middle and working classes of native-born Americans suffer, due to increased taxes and fees for public services.