The pool of illegal immigrants seeking to sign up for the Obama-era deportation amnesty for illegal immigrant Dreamers has dried up under President Trump, potentially offering a middle-ground solution as he tries to work his way out of a political and legal morass.

New sign-ups, which were averaging nearly 4,500 a month for most of last year, surged about the time of the election and transition from President Obama to Mr. Trump but have since dropped to about 1,800 per month, according to statistics from U.S. Citizenship and Immigration Services.

Renewals of expiring permits, though, remain strong, as the nearly 800,000 young adults already approved for the program fight to keep their tentative legal status intact, saying it has given them a foothold in American society and the economy.

Mr. Trump is facing a Sept. 5 deadline imposed by the state of Texas, where Attorney General Ken Paxton said the president must phase out the program, known in governmentspeak as DACA. If Mr. Trump doesn’t act, Mr. Paxton said, he will ask a federal judge to rule the program illegal.

Immigrant rights advocates have called on Mr. Trump to defend the program adespite the shaky legal footing. Otherwise, they say, the president will pay a tremendous political price. Democrats in Washington have taken up the cause as well.

“Ending DACA would be a moral disgrace,” Democratic National Committee Chairman Tom Perez said.

Mr. Trump has said he will make the decision on DACA himself, and he has several options: He could fight to preserve the program, continuing to approve two-year permits; he could phase out the program, allowing existing permits to remain in effect until they expire but not approving any new or renewal applications; or he could continue renewing already approved Dreamers but refuse to sign up any new ones.

Based on the latest numbers showing interest in applications waning, that last option could be attractive — though it’s unclear whether that would meet Mr. Paxton’s demand.

With a week to go until the deadline, Mr. Paxton’s office declined to comment Monday, saying the attorney general was occupied with responding to Hurricane Harvey.

The DACA program offers a two-year stay of deportation and a work permit, both renewable, to young adult illegal immigrants brought to the U.S. as children, who have kept a relatively clean criminal record and who have worked toward an education. DACA status and the work permit that accompanies it entitles Dreamers to driver’s licenses, Social Security numbers, some taxpayer benefits and, in some states, in-state tuition or even financial assistance for public colleges.

Opponents of the program — including Mr. Trump during the presidential campaign — say the program is illegal and sends the wrong message about immigration, carving out a special status for those who break the law.

They also point to problems with the program, which had protected suspected gang members and others from deportation initially.

In nearly five years of operation, through July 31, the government had approved 794,846 initial DACA applications and 923,714 renewals. Some of those were second renewals, which is why that number is higher than initial grants.

A total of 2,139 people have had their DACA status revoked through Aug. 14. Those revocations were results of a felony or serious misdemeanor conviction, multiple misdemeanors, suspected gang ties or other major public safety concerns.

Among those kicked out of the program were immigrants engaged in alien smuggling, domestic violence, drugs, sex offenses, weapons and drunken driving, said U.S. Citizenship and Immigration Services, the agency that oversees the program.

But the overall rate of wrongdoing is less than half of a percent, and the program’s defenders say those who get approved for DACA end up advancing in society.

A survey released Monday of thousands of DACA recipients found 97 percent are either in school or holding a job, and their average incomes jumped from $21,000 before DACA to $36,000 now. For those older than 25, it was an even bigger jump, from $22,000 to roughly $42,000.

Nearly two-thirds said they have been able to pursue educational opportunities that would have been denied them if they hadn’t been granted the tentative legal status, which in most states makes them eligible for public college, entitles them to driver’s licenses, and even qualifies them for some federal tax benefits.

Tom K. Wong of the University of California, San Diego, conducted the survey for the National Immigration Law Center, the Center for American Progress and United We Dream. They said 5 percent of DACA recipients have even started their own businesses, and 16 percent have bought homes.

Most of the Dreamers also have someone in their family who is an American citizen: 17 percent are married to a citizen, 26 percent have children who are citizens, and 59 percent say they have a sibling who’s American.

“DACA has been unreservedly good for the U.S. economy and for U.S. society more generally,” the report’s authors said.

Still, critics say the program is being abused.

Two Republican senators raised one example Monday, pointing to a loophole that lets DACA recipients who travel outside the U.S. with advance permission return to get on a speedy pathway to citizenship, as long as they have a qualifying family relationship such as a citizen child or spouse.

Sens. Chuck Grassley of Iowa and Mike Lee of Utah said the loophole, known as “advance parole,” has likely been used “dozens, if not hundreds” of times to help illegal immigrants cut at least 10 years out of their citizenship quest.

The loophole is known among immigration activists, and public colleges in California were urged to use it to help their illegal immigrant students under the DACA program to gain legal status.

The California-Mexico Studies Center advertises such a program, charging thousands of dollars to give Dreamers a chance to travel south to Mexico to qualify for advance parole. Part of the fees the program collects helps pay for “legal advice and filing assistance” in obtaining advance parole.

Another class of 35 students took advantage of the program earlier this month, visiting Mexico then returning back to the U.S. legally — making them now able to petition for permanent legal status if they have another qualifying relationship such as a citizen child or spouse.

“In short, advanced parole effectively eliminates a DACA recipient’s unlawful status and creates an otherwise unavailable pathway to citizenship,” the senators said in demanding more data on the practice from the Trump administration.

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