Here's the annual data from the US Border Patrol on apprehensions at the US-Mexico border over time.
The number of border apprehensions is often taken as a rough-and-ready measure of the number of people seeking to enter the US illegally. The decline strongly suggests that fewer Mexicans are trying to do so. Here's data from the Mexican government on the emigration rate from Mexico per 100,000 in the last decade. Notice that the big decline happens some years ago, even before the start of the Great Recession.
Data from the US side of the border on the Mexican immigrant population in the US actually shows a downturn in recent years.
Gonzalez-Barrera provided a useful figure in a longer report she wrote last fall at the Pew website about "More Mexicans Leaving than Coming to the U.S." (November 19, 2015).
These trends and the economic and demographic patterns behind them aren't new. I was blogging four years ago on the topic: "Net Immigration from Mexico Stops--or Turns Negative" (April 24, 2012). I wrote last year about "The Declining Number of Illegal Immigrants" (July 13, 2015) and about how "China and India Overtake Mexico for Inflow of US Foreign-Born Residents" (May 13, 2015).
How to limit or regulate the enormous inflow of immigrants from Mexico was a legitimate policy concern from the 1970s into the early 2000s. As Gonzalez-Barrera puts it, that migration was "one of the largest mass migrations in modern history." But now that flow has fallen substantially, and even reversed itself. The main issue now is be how we deal with the after-effects of that enormous mass migration and the immigrants who are already here--many of whom have been here for quite some time.