I'll give you a firm example. I'm close to a town of 20,000 in rural Minnesota, and the biggest employer is a well known turkey company. Their plants used to be staffed with primarily native (and being in Minnesota, white) people. It was menial, hard labor but it paid well because of that. By the 90s the plant was primarily staffed by illegal Mexican immigrants, and now it's almost entirely Somalians.

The jobs are repetitive, mindless, and it's cold, wet, and loud in there. The pay is barely above minimum wage. If the company didn't have access to those immigrants that are happy for any work at all, they would have been forced to raise those wages long ago. If people in the plant were paid, say, $15 an hour, the hourly workers in the office next door sure wouldn't be happy being paid the same amount. Their wages would have to be higher, which would mean the salaried folks would also want to be paid more.

That town is a perfect microcosm of how the massive amount of immigration our country has seen has kept wages stagnant.