i think that part of the issue for many is the perception of immigrants taking benefit money. i don't think they generally are eligible though and if someone could talk to this (like a Jeb Bush or a Marco Rubio) I think they'd go a long way.
the other part is taking jobs/depressing wages and that's true enough (if there were no immigrants willing to pick strawberries for a dollar a bucket or whatever, then they'd pay someone to pick the strawberries, they wouldn't just let them go to waste. and then strawberries would be more expensive... but the wages wouldn't have fallen). the nativists will continue to do well here until we're "back" to "normal" with wages and employment