It could be argued from a "leftist" position (whatever that means nowadays) that: it's mostly working class people that need to compete with immigrants. If the immigrants are undocumented or very poor, they are more likely to tolerate lower wages and unsafe working conditions, meaning that I (if I was a working class American) would have less negotiating power when it comes to my wages and work conditions, as there are plenty of people who would be happy to replace me. Also, working class people are more likely to meet with the immigrants that are engaged in illegal activities, whereas if you are middle-upper class or rich, you'll meet the educated, immigrants that maybe help your business growing or at the very least help you keep your household running.
I'm just trying to show a different "leftist" take, I don't really have a strong opinion on this issue as I believe there are good people on both sides and figuring out the best approach is basically impossible.