NEW ORLEANS — Immigrants who grew up in the United States after being brought here illegally as children were among close to 200 demonstrators who gathered Thursday outside a federal courthouse in New Orleans, where three appellate judges heard arguments over the Biden administration’s policy shielding them from deportation.

At stake in the long legal battle playing out at the 5th U.S. Circuit Court of Appeals is the future of about 535,000 people who have long-established lives in the U.S., even though they don’t hold citizenship or legal residency status and they could eventually be deported.

“I live here. I work here. I own a home here,” said María Rocha-Carrillo, 37. She traveled from New York to join the demonstration and was in the front row of a packed courtroom as the hearing started. She said she was brought to the U.S. at age 3 when family members immigrated from Mexico. She could not get a teaching certificate until the Deferred Action for Childhood Arrivals program allowed her to build a career in education.

Opponents of DACA weren’t in evidence among the demonstrators. But opponents, chiefly Texas and eight other Republican-dominated states, have said in court arguments and legal briefs that they incur hundreds of millions of dollars in health care, education and other costs when immigrants are allowed to remain in the country illegally.

As the hourlong hearing opened, Brian Boynton, arguing for the Biden administration, said the states have no standing to sue because they have demonstrated no harm caused by DACA. He said his argument is bolstered by Supreme Court decisions made since the 5th Circuit heard and rejected that contention in 2022.

Judge Jerry Smith pushed back. “I don’t understand how you get anywhere with that argument,” Smith said, stating that the Supreme Court precedents don’t contain unequivocal language that would require the appeals court to back off its previous finding.

Judges on the panel gave no indication of when or how they will rule. The case will almost certainly wind up at the Supreme Court.

Former President Barack Obama put the Deferred Action for Childhood Arrivals program in place in 2012, citing inaction by Congress on legislation aimed at giving those brought to the U.S. as youngsters a path to legal status and citizenship. Years of litigation followed. President Joe Biden renewed the program in hopes of winning court approval.

But in September 2023, U.S. District Judge Andrew Hanen in Houston said the executive branch had overstepped its authority. Hanen barred the government from approving new applications, but left it intact for existing recipients, known as “Dreamers,” during appeals.

Defenders of the policy argue that Congress has given the executive branch’s Department of Homeland Security authority to set immigration policy, and that the states challenging the program have no basis to sue.