Using our estimates and Census data we find that immigration (1990-2006) had small negative effects in the short run on native workers with no high school degree (-0.7%) and on average wages (-0.4%) while it had small positive effects on native workers with no high school degree (+0.3%) and on average native wages (+0.6%) in the long run. These results are perfectly in line with the estimated aggregate elasticities in the labor literature since Katz and Murphy (1992). We also find a wage effect of new immigrants on previous immigrants in the order of negative 6%.
When you take into account the fact that immigration is beneficial to the immigrants and to the recipients of their remittances, and that cracking down effectively on illegal immigration would entail large direct costs, this makes the case for a crack-down look extremely un-compelling. You're talking about very small short-term losses that are offset by very small long-term gains.