DILLEY, Texas >> When mothers and children streamed across the Texas border in 2014, the Obama administration devised a strategy to manage the influx, putting them in detention centers to convince others that illegal crossers would be caught and sent back.

But that strategy is now under intense legal and political attack, leaving the administration with limited options as it tries to stem a new rush of families fleeing and seeking asylum amid escalating violence in Central America.

This recent influx is compounding President Barack Obama’s troubles with immigration in his final year in office, as his efforts to achieve broad protections for immigrants already living in the country illegally have stalled in the federal courts and his fallback actions to try to quell a new border surge have alienated many political allies.

A federal court has ordered Department of Homeland Security officials to release children and their parents swiftly from detention, to pursue asylum claims in courts across the country. Those rapid releases have begun, with most mothers from a center here in Dilley and another nearby in Karnes City, Texas, being discharged in less than three weeks — although they wore ankle bracelets so officials can monitor their movements.

In recent days, Homeland Security agents have made arrests to deport families who arrived in 2014, and whose asylum cases failed in the courts, saying it is an alternative way to send a discouraging message to potential migrants in Central America.

The raids provoked a nationwide outcry from Latino and immigrant groups whose support the White House has long courted. The groups say women and children should be welcomed as refugees and not expelled to face the brutal street gangs they fled. And immigrant advocates — and all three Democratic presidential contenders — have said the administration should close the family detention centers entirely.

The Republican presidential candidates have pointed to the latest illegal flow as proof that Obama’s border enforcement has been hopelessly lax.

The new rush of Central American families began in late July, and on several recent days reached the heights of the 2014 influx. By Dec. 1, more than 17,000 migrants in families were caught along the border, more than double the number in the same period in 2014.

Homeland Security officials had started in June to reconfigure the two Texas centers, after mothers and children had spent long months in confinement.

Then in August, Judge Dolly M. Gee of U.S. District Court for the Central District of California ordered that migrant children could not be held in a locked detention center and had to be released, with their parents, “without unnecessary delay.” But the judge made an exception for an emergency due to an “influx,” for which she permitted children to be held for up to 20 days. Homeland Security officials seized on that exception, arguing that an influx existed even before the recent spike.

By doubling asylum officers and speeding legal procedures since late October, officials have been completing most initial asylum screenings in the two detention centers here in South Texas and releasing families within the 20-day limit.

Rather than shuttering the two centers, officials are adding 500 beds at the center in Karnes City, doubling its capacity. And they won their request for a federal appeals court to swiftly review Gee’s order to release migrants quickly. The order, Homeland Security Secretary Jeh Johnson said this week, “significantly constrains our ability to respond to an increasing flow of illegal immigration to the United States.”

On Monday, officials sent many of the more than 120 mothers and children who were arrested over the weekend to be deported back to the center in Dilley — set up to screen asylum seekers entering the United States — for final steps before they are sent out of the country.

But in a new legal setback for the administration, officials on Thursday had to halt the deportations of three Salvadoran mothers and their children arrested in the raids, removing them from an airplane at the last minute, after lawyers at the Dilley center won stays from the immigration appeals court. One woman had presented a doctor’s statement saying she had epilepsy and had three seizures since her arrest.

The new flow from Central America has several causes. Mothers here said gang violence had spread across El Salvador and Honduras in the past year, even reaching rural villages, with attacks increasingly against women.

Several women also said they had heard from the local radio and family members in the United States that women crossing the border were allowed to stay.

“I heard this country gives protection to single mothers with children,” said Karla Rodríguez, 30, who came from El Salvador with her 4-year-old daughter.

Rodríguez said she had been a manager at a busy upscale hotel in San Salvador. Gunmen seeking targets for kidnapping came to her home demanding the names of guests. They followed her to work, saying they would take her daughter if she did not give up guests. She fled.

Apprehended at the border, Rodríguez and her daughter passed a first screening interview with an asylum officer in the Dilley center and were released in 10 days. They planned to join her father, who lives in Delaware, and to fight for asylum there. Resting at a shelter in San Antonio before continuing her journey, she was elated, despite the heavy band on her ankle. “I trust in God, who brought us this far,” she said.

Inside the centers, officials have set a frenetic pace. Women and children have medical screenings at in-house clinics within 24 hours after arrival and dental checkups within two weeks, members of the medical staff said. Everyone gets vaccinations.

Most women have interviews with an asylum officer within six days — warp speed in the immigration system. The interviews are for officers to determine if a migrant’s fears of returning home are credible.

Most women are persuading officers that their fears are real. Of 7,892 migrants admitted to the two centers in the three months ending Nov. 1, only 41 were rejected and deported, official figures show.

But many women are not connecting with lawyers to help them with their cases. The tempo is faster than lawyers here, mostly volunteers, can handle. Court statistics show that asylum seekers with lawyers are far more likely to go to court and win their claims. Yet at the Karnes City center one day, two frantic lawyers scrambled just to make last-ditch contact with bewildered women who had lost several legal rounds.

“We’ve been running around trying to prevent women from being deported before they even had a real opportunity to express their fears,” said Stephanie Cordero, a volunteer from the Legal Aid Society of New York.

One of those women was Rosa Elida Castro, 26, a Salvadoran who said she was preyed upon by a gang because they assumed she had inherited money after her mother died. An ex-husband had sexually abused her, hounding her out of her home.

“If we weren’t in danger,” she said, crying, “why would we have come?”

© 2016 The New York Times Company