President Trump’s new budget retreats on his campaign promise to require all U.S. businesses to use E-Verify to check their new hires, signaling the White House’s surrender on one of the best tools to shut down the jobs magnet that spurs illegal immigration.

In the budget, released Monday, Mr. Trump says he backs the current mostly voluntary version of E-Verify.

Gone is language from the previous two budgets calling for “mandatory nationwide use.”

Immigration experts said the administration is setting the table for the 600-page immigration proposal Jared Kushner, the president’s son-in-law, has been preparing for months. That plan would shift American immigration to a more business-friendly system — and, sources say it does not include mandatory E-Verify.

Having the budget say otherwise could have been an embarrassing conflict, said Jessica Vaughan, policy studies director at the Center for Immigration Studies.

“It had to be changed to stay consistent with Kushner’s proposal, which is at odds with what the president has been saying,” Ms. Vaughan said. “It’s a takeover of the president’s immigration agenda by the special interests who benefit from illegal immigration.”

E-Verify, run by Homeland Security, is an electronic system available to employers to run their new hires’ information. They are told, usually instantaneously, whether the person is work-authorized.

Currently it’s voluntary for most companies, though federal contractors are supposed to use it, and some states have passed laws mandating use as well.

Though not infallible, the system is considered the best way to prevent illegal immigrants from taking jobs, and has long been the Holy Grail for security advocates and those pushing for stricter immigration limits.

The Trump budget retreat was dismaying to them.

“I hope it was simply an oversight, rather than an indication that the Trump administration is abandoning the most effective tool we have to limit illegal immigration and protect the jobs and wages of American workers,” said Rosemary Jenks, vice president at NumbersUSA, which runs television commercials backing use of E-Verify.

The Obama administration had also supported mandatory E-Verify, though only as part of a broader legalization of illegal immigrants.

Obama officials figured mandating E-Verify before then would hurt those illegal immigrants already in the U.S., denying them jobs or locking them in with their current employers, who could then exploit their captive labor.

The White House budget office did not respond to multiple messages asking about the change.

Homeland Security responded to an inquiry by forwarding a press release that didn’t mention E-Verify. The department then ignored a follow-up email.

Mandatory E-Verify had been part of Mr. Trump’s immigration policy dating back to the campaign. It was Priority No. 9 on his 10-point immigration plan released in August 2016, and was part of his immigration plans in 2017.

Trump budgets released in 2018 and 2019 both called for mandatory nationwide E-Verify.

Last year’s document had a section labeled “Reduces illegal immigration work incentives.” It read: “The employment of illegal aliens by companies is a violation of the law, harms U.S. workers, and contributes to human smuggling, document fraud, identity theft, money laundering, and labor violations. The Budget proposes mandatory, nationwide use of the e-Verify system, an online tool that allows businesses to determine the eligibility of their employees to work in the United States.

This year’s section is labeled “Maintains a critical employment verification system,” and the section about “mandatory, nationwide use” is deleted.

This year’s budget also cuts $3.7 million from E-Verify’s funding. The budget says that comes from savings due to efficiencies from using cloud computing, and doesn’t mean any loss of capabilities.

Ms. Vaughan said the administration is hoping people see that they’re continuing the current voluntary system, but don’t realize they’ve retreated on the promise of mandatory E-Verify.

Ms. Vaughan said making it mandatory is critical because otherwise companies won’t sign up, fearing their competitors would gain an advantage.

“I’ve had this conversation with a number of big employers. If you ask them why they haven’t signed up for E-Verify, the answer is ‘Because I don’t have to,’” she said.

Indeed, it took a series of scandals to get most of Mr. Trump’s own companies to sign up, with illegal immigrants coming forward to say they’d been employed for years at Trump resorts. One even recounted making the bed in Mr. Trump’s own room.

After those stories, the Trump Organization rushed to sign up for E-Verify.

But the president himself suddenly had misgivings.

In an interview with Fox News in May 2019 he said his business tried to use E-Verify when it was building the Trump International Hotel on Pennsylvania Avenue, but it made it too tough to hire people.

“We would go through 28 people — 29, 30 people before we found one that qualified,” he told Fox.

“So it’s a very tough thing to ask a farmer to go through that. So in a certain way, I speak against myself, but you also have to have a world of some practicality,” Mr. Trump said.

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