A plan to slash legal immigration backed by President Donald Trump would cause U.S. GDP and jobs to dip over time, according to an analysis by the University of Pennsylvania's Wharton business school.

The RAISE Act would lead GDP to drop by 0.7 percent by 2027 relative to current law, with 1.3 million fewer jobs, the Penn Wharton Budget Model report said. By 2040, it would reduce GDP by about 2 percent, with 4.6 million fewer jobs.

The bill, crafted by Sens. Tom Cotton, R-Ark., and David Perdue, R-Ga., is expected to cut legal immigration in half. The plan aims to make job skills, rather than family connections, a priority for people to obtain legal permanent residency. It also would slash the number of refugees coming to the U.S.

Cotton's office disputed the report and criticized its methodology. Cotton's communications director, Caroline Rabbitt, said the analysis used data that "misses nearly half of all green cards."

"This gross undercounting of green cards is an understandable mistake for people new to immigration, but it's embarrassing for purported 'experts' and shows that their projections are unreliable," she said.

A White House official, who asked not to be named, responded by taking issue with the model used by Wharton, saying it has "major methodological faults." Those faults are centered on the impact of reduced immigration on American workers.

The official said that RAISE will make more jobs available to existing U.S. citizens. The official points out that the Wharton model calls for 5 million fewer jobs but 10 million fewer immigrants. So, taking the model at face value, the official said, means whatever job losses could occur from the new immigration plan would be overwhelmed by the reduction in foreign workers.

"There will be a higher percentage of the (existing) population employed under the RAISE Act," the official said.

The Penn analysis said that on a per capita basis, GDP would be about 0.02 percent higher in 2027 under the law. But it would end up about 0.3 percent lower in 2040.

It would initially rise "because the capital stock will be similar to before the reform while the pool of workers will be smaller," according to the Wharton school analysis. It would eventually change because, "over the long run, immigrants work and contribute to savings," the report says.

"The RAISE Act also reduces employment because the domestic worker participation rate won't increase enough to fill the jobs that would have been held by immigrants who are no longer allowed in the country," the report says.

Trump and the senators have defended the plan, arguing it will lead to a more "merit-based" immigration system. The president contends the bill would "increase wages and save taxpayers billions."

The question of whether foreign workers reduce U.S. wages and take jobs, especially low-skilled jobs, is at the heart of the immigration debate. Supporters of the bill cite immigration as a main reason why low-skilled wages have declined over the past several decades. Immigration supporters argue that cutting back on immigration would reduce potential growth as foreigners make up a greater and greater share of total U.S. population growth.

The bill has little chance of becoming law, as various Republican lawmakers from states reliant on lower-skilled immigrant labor have spoken out against it.

A spokesperson for Perdue did not immediately respond to CNBC's request for comment.