This is a strawman argument, because there isn't much cross-sector competition between skilled, unskilled vs. professional workers, except perhaps in times of economic crisis when the unemployment rates is in the double digits. The issue at hand isn't that truck drivers are paid less than medical doctors - the issue (which is a problem from the standpoint of management and pro-immigration politicians) is that American truckers demand American truck driver wages rather than Guatemalan truck driver wages, just as American computer programmers won't work for Chinese computer programmer wages.
I strongly support the crackdown on illegal immigration and the enforcement of existing immigration laws. I have been retired for a few years now - so market conditions may well have changed. My mid-sized consulting company, based in Boston, ended up hiring programmers from Mumbai and Katmandu as well as local programmers. The Federal Government required us to pay prevailing local wages before we could hire foreign nationals. We were strictly speaking not a tech business but needed multi-skilled programmers to develop on-line software apps and tools. We could not find them. The H1B folks we ended up hiring were outstanding - they knew their technical stuff, they were creative and were committed to getting the job done - as were the US folks. They both were full members of the team and got along well with colleagues and clients. One has worked at the company for nearly 20 years, the other left for LA after 8 years.
I worked with the NSF on STEM education and utilization issues and attended various IEEE conferences on HR and staffing issues. Sadly I found an inordinate level of straightforward xenophobia among tech people back in the 1980s. Some of these comments indicate that it has not decreased.