That is a policy problem. The answer, then, is not to further cripple the market by limiting the number of available workers, but to eliminate the interference in the market in the first place, like welfare and unemployment and whatnot.
The wellbeing of this country and its communities and its people is more important than the purity of free market libertarianism. To that end we interfere all the time in the "free market" for child pornography, crack cocaine, plastic guns, Kevlar piercing ammo, and streetwalkers.
Rampant illegal immigration is a direct threat to the well being of this country. It is not in the interest of this nation to see its standard of living reduced to a Third World level, whatever the purity of the "free market".