That's pretty much all politics and no economics.

The division of labor, coupled with the massive increase in productivity (both demanded and supplied) will create all the jobs needed.

If you want to see the fallacy a little more clearly, replace "immigrants" with "babies born" and take a look at history to see how economies always adapt to changes in population. On top of that, take a look at where the jobs are needed and how it actually helps to free up workers to be put into more productive, more specialized fields.