Via Dylan Matthews, the Hamilton Project has the great summary chart (above) comparing the findings about the short-term economic impact of immigration from two major studies by economists. I'm more of an Ottaviano-Peri man than a Borjas-Katz man because I believe in complementarity, the idea that immigrant workers increase the demand for skills (English language competence, for example) that even 'unskilled' U.S.-born workers have.
What it also shows you is that the actual economics of immigration are totally irrelevant to the political debate. The voters most likely to oppose high levels of immigration are precisely the people who Borjas and Katz say benefit from it economically. Meanwhile, immigration supporters and especially Spanish-dominant Latinos often feel the negative wage impact of immigration, since that's where complementarity plays the least role. In other words, if the immigration issue were about economics, then you'd see white working-class voters clamoring for amnesty and open borders while SEIU and MALDEF emphasized the need to secure the border before taking any further steps.
Of course you don't see that at all, which is why I strongly recommend that everyone read Mickey Kaus' points four and five against amnesty, which actually get to the crux of the issue.
He has a fear that immigrants from Latin America are "different" from earlier waves of immigration thanks to Mexico's geographical proximity to the United States and the existence of Univision and other Spanish-language media. That is, to my way of thinking, totally nuts. But it explains why there's enormous skepticism of immigration among white working-class voters who, research shows, benefit from it economically. It also explains why Cuban-Americans from Marco Rubio to Bob Menendez to yours truly feel emotionally invested in the issue, even though immigration restrictions aren't really applied to Cubans. Unfortunately, immigration scolds seem to be excessively afraid to voice their real concerns about this, which makes it difficult to address them with either evidence or policy concessions. Instead, we're stuck in a mostly phony argument about wages that does nothing to ease people's real fears about nationalism and identity.