Would there be a flood of new immigrants if comprehensive immigration reform passed?

In yesterday's New York Times, Damien Cave wrote an uncommonly good article about immigration.  One of the critiques of a path to citizenship under consideration is that it would just draw many more undocumented immigrants who will flood into the country to try to benefit from the new law.  Cave's article shows this simply would not be true based on two factors.

First, the most powerful evidence that a legalization program would not trigger a lot more immigrants is that the last program in 1986 did not precipitate a surge.  And why is that?  Because the law was written in a way that only those that could prove (through utility bills/rental leases/pay stubs) that they had been in the country for a certain amount of time could qualify for the benefits.

Second, Cave's article correctly points out that the root cause and magnet for undocumented migration is jobs, not immigration status.  The immigrants come here to work, not to gain a legal immigration status.  As Wayne Cornelius who is cited in the article explains:

The great wave of Mexican migration to the U.S. in the second half of the 1990s and early 2000s was driven by the abundance of jobs generated by the U.S. economic boom of this period...Any delayed effects of the 1986 amnesty were inconsequential compared with the incentives created by U.S. job growth."

Cornelius, one of the great scholars of Mexican migration to the U.S. is absolutely right.  The magnet for undocumented and even much documented migration has been jobs--not a free public education, not a drivers' license, not medical care--all which are secondary to jobs, jobs, jobs.