Lie #1: Illegal aliens take jobs Americans won't do.
Truth: Americans are willing to do most jobs at a fair wage, but they won't do those jobs at "slave wages" or minimum wage. Thus, American workers are constantly replaced by illegal aliens willing to work for half or a third of what American workers once received. These jobs that once afforded a middle class life style now only offer illegal alien workers poverty level wages, resulting in the shrinkage of the "American Middle Class" and the enormous growth of an ever-increasing "underclass" dependent on government entitlements.
Surely the way to prevent this happening is to ensure the immigrants have to be paid fairly? That way there'd be no financial motive to hire them over American citizens.