There's some truth to this. Immigrants who get hooked on welfare and other social programs normally vote for Democrats who push those programs. It becomes something of a partnership that helps Democrats gain votes.
Interesting how all we hear about is the economic cost of immigrants, when the benefits to US citizens far outweigh the costs.
4% immigrant unemployment is noise level.
US businesses would shut down without cheap labor and the whole business would move south of the border.
We'd all be paying more for goods and services (cut grass, nanny kids, pick crops, manual labor).