Others in politics have put a finer touch on it. “Absent visa reductions, the annual rate of immigration, the total level of immigration, and the percentage of the country that is foreign-born will continue surging every single year,” Sen. Jeff Sessions (R-Ala.) and Rep. Dave Brat (R-Va.) said in a letter last year.

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But the problem with this view, as Ira Glass noted in a recent episode of the podcast “This American Life,” is that it really is not true.

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Although the flow of illegal immigrants across the border may be higher than some want, it has not risen in recent years. In fact, as a new report from Pew Research Center shows, the number of illegal immigrants working or looking for work in the United States has been roughly flat between 2009 and 2014, at about 8 million people. There is some movement across the border, but it's hardly massive: About 350,000 illegal immigrants have entered the country each year, but the same number have also left the country.

Together, unauthorized immigrants make up 5 percent of America's civilian labor force, a proportion that is down slightly since 2009, Pew says. The unauthorized immigrant population in the United States grew rapidly in the 1990s and early 2000s, but those trends changed dramatically with the financial crisis.

Some sources, such as the Conservative Review, have reported a surge in immigration after 2014. It’s true that data from one survey, the 2015 Current Population Survey, showed an increase in Mexican immigration. But Jeffrey Passel, a senior demographer at Pew, says that over time, it has become more clear that results from that survey were an anomaly — which is something that occasionally happens with individual surveys — rather than an indication of a big migration event.

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“Those numbers were not consistent with anything else we’ve seen,” Passel said.

Although that 2015 survey showed an increase in Mexican immigration, the 2015 American Community Survey, which is based on a much larger sample, showed that the total number of Mexican immigrants in the country is virtually unchanged over the 2010-2016 period, Passel said. The 2016 Current Population Survey, labor-force surveys of out-migration in Mexico and apprehensions of undocumented Mexicans at the Southern border all pointed to the same trend — that the number of Mexican immigrants in the United States has been roughly constant for many years.

“By the end of 2015, there’s no indication of this surge. If there had been a surge, there was a surge back by the end of the year,” Passel said.