This has always - always - been the opinion of right wingers. "Immigrants" are going to take your job!" It is not true, has never been true, and most economic studies have found only a very small effect in the lowest paid professions, and none in other professions. When employers turn to undocumented workers, it is because they can't find native born workers at the rate they want to pay.

I've done substantial work on immigration and assimilation. This argument has a few sincere economists behind it, but not many. Most of this is simply another right wing fear tactic creating a strawman in hopes to fire up the racist base.