President Trump has adopted a blunt new message in recent days for migrants seeking refuge in the United States: “Our country is full.”

To the degree the president is addressing something broader than the recent strains on the asylum-seeking process, the line suggests the nation can’t accommodate higher immigration levels because it is already bursting at the seams. But it runs counter to the consensus among demographers and economists.

They see ample evidence of a country that is not remotely “full” — but one where an aging population and declining birthrates among the native-born population are creating underpopulated cities and towns, vacant housing and troubled public finances.

Local officials in many of those places view a shrinking population and work force as an existential problem with few obvious solutions.

“I believe our biggest threat is our declining labor force,” said Gov. Phil Scott of Vermont, a Republican, in his annual budget address this year. “It’s the root of every problem we face.

“This makes it incredibly difficult for businesses to recruit new employees and expand, harder for communities to grow and leaves fewer of us to cover the cost of state government.”

Or if you look at a city like Detroit, “many of the city’s problems would become less difficult if its population would start growing,” said Edward Glaeser, a Harvard economist. “All sorts of things like the hangover pension liability become much more solvable if you’re actually looking at new people coming in.”

A road less traveled in Rutland, Vt., last spring. Vermont’s governor has described the state’s shrinking labor force as “at the root of every problem we face.” CreditCaleb Kenna for The New York Times

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This consensus is visible in official government projections. The Congressional Budget Office foresees the American labor force rising by only 0.5 percent a year over the coming decade, about one-third as fast as from 1950 to 2007. That is a crucial reason that economic growth is forecast to remain well below its late 20th-century levels.

And that, in turn, is reflected in the national fiscal outlook. There are now 2.8 workers for every recipient of Social Security benefits, a rate on track to fall to 2.2 by 2035, according to the program’s trustees. Many state pension plans face even greater demography-induced strains.

In smaller cities and rural areas, demographic decline is a fundamental fact of life. A recent study by the Economic Innovation Group found that 80 percent of American counties, with a combined population of 149 million, saw a decline in their number of prime working-age adults from 2007 to 2017.

Population growth in the United States has now hit its lowest level since 1937, partly because of a record-low fertility rate — the number of children born per woman. The United States increasingly has population growth rates similar to slow-growing Japan and Western Europe, with immigration partly offsetting that shift.

The Trump administration has portrayed the surge of asylum seekers at the southern border as a crisis, and applied aggressive tactics to deport undocumented immigrants already in the United States. But it has also announced plans to issue up to 30,000 additional H-2B visas for temporary workers.

“That immigrants keep showing up here is a testament to our freedom and the economic opportunity here,” said Matthew Kahn, an economist at the University of Southern California. If immigrants weren’t trying to come — if they believed the United States to be full — that would be a problem, Mr. Kahn said.

A particular fear, said John Lettieri, president of the Economic Innovation Group, is that declining population, falling home prices and weak public finances will create a vicious cycle that the places losing population could find hard to escape.

He proposes a program of “heartland visas,” in which skilled immigrants could obtain work visas to the United States on the condition they live in one of the counties facing demographic decline — with troubled counties themselves deciding whether to participate.

Although some of the areas with declining demographics are hostile to immigration, others, cities as varied as Baltimore, Indianapolis and Fargo, N.D., have embraced the strategy of encouraging it.

“One of the key solutions is to welcome immigrants into these communities,” said Brooks Rainwater, director of the National League of Cities’ Center for City Solutions.

Many parts of the country that are growing in population and that are more economically dynamic have depended on the arrival of immigrants for that success.

Sun Belt metros like Dallas and Phoenix have been built on the logic of rapid expansion — of quickly built homes, of poached employers, of new highways paved to ever-newer subdivisions. Their economic development strategy is growth. Their chief input is people — the more, the better.

“Growth cities need immigrants to continue their growth,” said Joel Kotkin, executive director of the Houston-based Center for Opportunity Urbanism, which promotes policies to help cities grow. “The older historically declining cities need immigrants to reinvigorate their economies. And the expensive cities need them because, frankly, white people, African-Americans and middle-class people are leaving for more affordable areas.”

As many industrial cities have lost population since the mid-20th century, Americans have built whole new metropolises on land that was virtually empty then. The Las Vegas metropolitan area, with more than two million people today, had barely 50,000 in 1950.

Still, only about 3 percent of the country’s land is urbanized.

America’s metropolitan areas remain among the least dense in the world, said Sonia Hirt, a professor of landscape architecture and planning at the University of Georgia. Nationwide, the United States has less than one-third of the population density of the European Union, and a quarter of the density of China.