I run a version of this post every few years.  Here is the 2015version. The Economist liked the chart in that version of the post, replicatingit here.  The data leads to the unimpeachable conclusion that the H-1B visa doesnot take away US workers jobs.  The H-1Bvisa fills jobs in industries where it is nearly impossible to find qualified US workers.
In 2009, a mere 9,000 H-1Bs were received in the first month ofH-1B processing.  It would be 264 daysbefore the H-1B cap was reached. In 2010, it took 300 days until the H-1B capwas reached.  In 2011, there were 236days between the April 1, 2011 cap opening and the November 23, 2011 cap beingreached.  Not coincidentally, the USemployment rate from 2009-2011 ranged betweeneight and ten percent.
On the other hand, the H-1B cap was reached on the very first dayin 2007, 2008, and every year since 2013, mirroring the low unemployment rate.

My chart from 2015.
 
The lack of H-1B petition filings in years when the unemploymentrate is high is compelling evidence against the argument thatinternationally-trained workers are being used to displace American workers andlower US workers’ salaries.
Why?  Because if H-1B visalabor was being used primarily to lower US workers’ salaries, then H-1B filingnumbers would not correlate with US unemployment rates.  If anything, the reverse would happen becausethe incentive to reduce workers’ salaries is likely greater in a recessedeconomy, not less.
The President and his hackneyed hatchet man Steven Millerdo not believe in data.  The Presidentrecently signed a ridiculous Executive Orderlimiting permanent residency visas (green cards) for 60 days.  The Order accomplishes nothing, but may setthe table for a broader visa ban, which could include H-1Bs and other temporaryvisas.
Millerrecently said that “the most important thing isto turn off the faucet of new immigrant labor,” as if this will save Americanjobs.  It won’t.  Limiting immigrant labor has never saved asingle American job and it never will. 
Miller is plainly not interested in the Americaneconomy.  He gave away his real interest whenhe said that the temporary banwould limit “chains of follow-on migration.”  That is Miller’s real interest: stopping allforms of legal migration, which he believes waters down American culture.  His goal is to centrally plan American culture in his image.
Politicians should see employment visas for what they are — tools forgrowing industries to fill labor shortages.  Organizations — and governments — workbetter when they work on data and not on nonsense and rhetoric.
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Here is an updated version of the chart.  The most important part of the data looks atthe spike in unemployment from 2008-2014.  It is worth nothing that since 2014 we have had record levels of H-1Bpetitions, and full employment.

(Click on the chart to expand)