Tell that to the millions of framers, roofers, and general laborers in the construction industry. And that’s just for starters. It’s not a question of how productive or self supporting an “economic refugee” may be. The fact is they will be willing to work for much less, and as good little Libertarians we can’t fault the employer, or the “migrant” as they contribute to dragging the country to the same status the “economic refugees” escaped.
The primary and overwhelming reason illegals are willing to work for much less is that they are subsidized enormously and in practice exempt from a wide range of regulations, whereas US labor is not. If they had all the same costs of a US worker, they’d need to work for a similar price.