NEW ORLEANS — Government lawyers labored on Friday to persuade federal appeals court judges here to allow President Obama to move ahead with sweeping initiatives to protect immigrants in the country illegally. But the judges’ questions seemed to make it ever more unlikely that the president’s programs, which he has hoped would be a central piece of his legacy, would start any time before the last months of his term, if at all.
A panel of three judges of the United States Court of Appeals for the Fifth Circuit heard arguments in a lawsuit by Texas and 25 other states challenging executive actions Mr. Obama announced in November that would give temporary reprieves from deportation to as many as four million immigrants and also permit them to work.
In February, a federal district judge in Texas blocked the programs. On May 26, a panel of the Fifth Circuit denied the administration’s emergency request to cancel that injunction, with two judges supporting the denial and one dissenting. This time, the judges heard a broader appeal by the government on the challenge to the executive actions.
But even though the judges issued no decision on Friday, it seemed highly probable that the administration would lose. By a stroke of bad luck for Mr. Obama and good fortune for the states bringing the lawsuit, two judges on Friday’s panel — Judge Jerry E. Smith and Judge Jennifer Elrod — are the same conservatives who ruled against the administration in May. Court officials said both panels had been randomly selected, well before the administration even brought its case to the Fifth Circuit.
A setback now would be decisively damaging to the president’s argument that he has full authority to carry out the vast programs nationwide and would leave the administration little choice but to take the case to the high-stakes and slow-moving deliberations of the Supreme Court and to hope for a favorable ruling before the end of its term in June of next year.
Mr. Obama has run into far deeper legal trouble than officials anticipated when they decided last year to create a program by executive action, without approval by Congress, extending deportation deferrals and work permits to millions of undocumented immigrants who are parents of American citizens or legal residents.
Judges Smith and Elrod peppered the government’s lawyer, Benjamin C. Mizer, a principal deputy assistant attorney general, with skeptical questions about his contention that the administration had ample authority to focus immigration enforcement on deporting immigrants who commit crimes or threaten national security, and to defer deportations of those who pose little risk to public safety and have families in the United States.
Referring to Homeland Security Secretary Jeh Johnson, Judge Elrod asked, with a note of incredulity, “So the secretary has boundless discretion to give work authorization to whomever he wants and it is not constrained by congressional law?”
The administration’s arguments about the president’s powers have faltered over Texas driver’s licenses. Texas has said it would be a burden to have to pay at least $130 each for driver’s licenses for as many as 500,000 unauthorized immigrants who could obtain the licenses if they received deferrals under the president’s programs. Judge Smith, in his 42-page opinion in May, agreed.
But Scott Keller, the solicitor general of Texas who argued for the states, drew concern from all three judges when he said Mr. Obama’s programs were not only a “sweeping assertion of executive power” but were breaking the law. His arguments raised complex new issues for the judges to consider this time around, probably extending the time before they rule.
The judge who sided with the administration in May, Stephen A. Higginson, was not on the panel on Friday. The third member was Carolyn D. King, nominated in 1979 by President Carter, and formerly chief judge of the Fifth Circuit. She sharply questioned Mr. Keller, the Texas lawyer.
Jurists and legal experts familiar with procedures in the Fifth Circuit court said it was coincidence — and very unusual — that the two panels hearing different phases of the immigration lawsuit included two of the same judges. Judge Smith is an outspoken conservative who has wrangled publicly with Mr. Obama over the extent of the president’s powers.
Court officials said the chief judge, Carl E. Stewart, was so concerned it might appear that the court had acted improperly to influence the immigration case that he ordered a clerk to flip a coin in the presence of witnesses to decide which of two panels scheduled to hear cases this week would handle the Texas lawsuit.
The debate in the hushed, elegant courtroom was overwhelmed several times by the sounds of drums and horns from about 600 protesters from immigrant rights groups in the street outside, including people who traveled from California, Arizona, Texas and Alabama.
A smaller group sat down in the street in front of the offices nearby of the federal Immigration and Customs Enforcement agency. A spokesman for the protesters said 14 people were arrested, but were quickly released.
“People are still getting deported every day,” said Saket Soni, the executive director of the New Orleans Workers’ Center for Racial Justice. He said the demonstrations were intended to “supply hope to the movement and signal to ICE there is much more of this coming.”
The administration has faced even more serious legal trouble with the federal district judge in the case, Andrew S. Hanen. He has chastised officials for failing to inform him that more than 100,000 deferrals with extended three-year terms had been issued under the president’s programs to young immigrants before he imposed the injunction. He ordered the government to cancel and collect about 2,000 three-year work cards that were granted to youths after the injunction took effect and to issue new cards with the original term of two years.
Infuriated that the administration had not collected every card, on Tuesday, Judge Hanen issued an unusually harsh rebuke, calling the officials’ conduct “unacceptable and completely unprofessional.” In an action federal judges rarely take, he ordered the secretary of Homeland Security, Mr. Johnson, to appear in person in his Brownsville court on Aug. 19 to explain why the judge should not find him in contempt.