Macroeconomic Advisers co-founder Joel Prakken says the economy should grow at about 2 percent next year, but already it could see a dent if immigration is slowed. "What's behind that projection is the assumption of labor force growth and productivity growth ... that is a combination of assumptions about the participation rate and the growth of the population. Our assumptions of the population come from the Census Bureau," he said.

Statistics provided by the U.S. Census Bureau on assumptions about population growth and immigration are rolled into economists' forecasts for GDP. Economists say there are already worker shortages in some areas, and the problem could get worse quickly.

"It's half of labor force growth today. Going forward it's a bigger drag. We have yet to meet the critical mass of baby boomers retiring. That's still ahead," said Diane Swonk, chief economist at DS Economics.

Immigrants are responsible for nearly half the population growth of the United States, and by extension that also means they are a sizable part of the growth in the U.S. labor force.

Trump Wednesday embraced legislation put forth by two senators to cut legal immigration into the U.S. in half within a decade and base entry on education, language ability and job skills that would benefit the country.

President Donald Trump could limit his own plans to grow the U.S. economy in half becomes law, economists said.

"If you cut the labor force growth in half you probably take two to three tenths of a percentage point off GDP growth every year over the next decade," Prakken said. He said that would also impact the 3 percent growth pace the Office of Management and Budget is forecasting for 2020 and beyond. The Trump administration forecasts 2.4 percent growth next year.

Prakken said immigrants are probably a bigger portion of the growth in the labor force, since the U.S. population is aging, immigrants are generally younger and many come to the U.S. specifically to work. Industries that could see big impacts would be agricultural, leisure and hospitality and construction, he said.

"There would be spot shortages," he said.

He said one adverse impact could be that companies in some industries could move operations outside the U.S. if they can't find enough workers, which would be opposite the Trump administration's efforts to attract more jobs.

"It's another one of these cases where [a law] could have adverse consequences that move in the opposite direction of some other initiative the administration is trumpeting," he said.

There are some workers who would find more jobs in their field because of fewer immigrants, but Prakken said it's a relatively "small slice" of the labor force.

Trump's support for this legislation is in line with his campaign promises to boost opportunities for American workers.

Prakken said the natural increase in the population, meaning those that are born in the U.S., is expected to come down due to aging of the population and fertility rates.

"The real issue is what would it do to potential growth in an economy where we need more people to replace retirees," said Swonk. "You're closing another door to offset the drag from an aging population."

Prakken said the proposed bill's limit on immigration would reduce it to roughly half the 1.1 million immigrants who arrived in 2015.

"The effect gets bigger over time because the Census assumptions for immigration keep growing and growing and growing, and the bill would not allow any growth," he said.

In its forecast in future years, the Census Bureau shows immigration growth well above the current 1.1 million annual immigrants allowed entry for the past several years. Prakken shows in red the estimated difference between the current number of immigrants allowed into the U.S. and the Census Bureau estimates.