Most immigrants (legal and illegal) are not Indian software engineers working at Google. They are low skill/poorly educated and got in on refuge status or because they have a family member already in the country. They work as taxi drivers, construction workers, cashiers, etc. It's not a huge leap of imagination that a constantly increasing low skill labor supply is to the detriment of current workers in these fields (many of whom might be immigrants themselves). 29% of immigrants lack a high school degree or equivalent GED and are disproportionally represented in the service industry, construction, maintenance, and other blue collar positions.
For example: https://www.migrationpolicy.org/sites/default/files/source_i...
So yes, it is likely that immigration rates have a negative effect on the wages of native workers in low barrier of entry positions. You'd have to suspend disbelief to accept the narrative that there is no impact.
source: https://www.migrationpolicy.org/article/frequently-requested...
