The economics of this issue for workers are as simple as simple as supply and demand. Other things being equal, if the supply of workers is increased, the market price (wages) for workers will fall. Millions of illegal aliens cannot just be dumped into a labor market without depressing wages.
There are people who benefit from illegal immigration. Obviously, the employers who illegally hire them benefit because their costs are reduced. And, all of us as consumers benefit to some extent from those lower costs.
But American workers and taxpayers (particularly local taxpayers) are taking a bath. We just can't expect them to be happy about that. ;-)