Fox business, “White House reports” and “2 million jobs”. Sounds fake off top
The Bureau of Labor Statistics, which compiles the Labor Department's monthly jobs reports, doesn't evaluate the immigration status of workers, and therefore the reports likely include unauthorized immigrants in the data.
Though the household survey used by the BLS differentiates between foreign- and native-born workers, it doesn't ask about legal status — meaning that the decline in foreign-born workers could also be affecting those who were born overseas and have legal authorization to work in the U.S.
At no time in history would a fully functioning literate adult who wants to work be competing for work with an illegal.