“Thank God we have immigrants coming in,” she said. “We’re hiring them as fast as they come.”

More than a million immigrants enter the United States every year, most of them through authorized channels. Altogether, there are more than 44 million immigrants, or 13.6 percent of the population. The share is significantly higher than it was in 1970, but below the peak in the 1890s, when millions of Europeans crossed the Atlantic Ocean.

President Trump has publicly resisted the argument that the nation needs more immigrants. “Our country is full,” he said during a visit to the border this spring. “We can’t take any more.”

But Mr. Trump’s proposals have at times deviated from his statements. In May, he proposed revamping legal immigration, without reducing the overall level, by giving preference to immigrants with skills, education and job offers, instead of people with family ties.

There is no way to figure out precisely how many more immigrants the national economy could easily absorb without a lot of guessing. Powerful forces like technology, globalization and the decline in union strength can heave economies around willy-nilly, benefiting some workers and hurting others, regardless of immigration.

Despite a decade-long expansion and a low official jobless rate, the income gap is widening, and many Americans struggle to find stable employment and middle-class wages.

A common complaint is that immigrants snatch jobs from native-born Americans, particularly those who didn’t finish high school. This group is already most likely to earn the minimum wage or be out of work.

There is scattershot evidence that in some places immigrants can press down wages at the lowest end of the income scale, but that is not typical.