Ms. Vargas quit her job at the steakhouse and returned to a place she had worked before — the motel where her grandmother is a maid. She cleaned rooms and pressed shirts for $9 an hour, and got a second job as a waitress at another restaurant in Cotulla, earning $5 an hour, plus tips. Some days she worked at both jobs.

But the family was falling behind financially. It cost more than $2,400 to bail Mr. Olivares out of jail. Ms. Vargas had paid $820 but still owed the rest. When Ms. Salinas had hired a neighbor to rip out the cracked particleboard floor in the trailer and put in faux-wood flooring, one of Ms. Vargas’s children had thrown the man’s car key into a smoldering fire they had made outside to burn some trash. Ms. Vargas owed the man $300 for a new key and the cost of a tow. Her cellphone service was cut off when she failed to pay the bill.

Ms. Vargas dreams her children will have a better life. “I wouldn’t want my kid to be in no motel and no restaurant, getting paid minimum wage,” she said.

One Wednesday evening, Ms. Vargas drove her children and her grandmother to the Living Faith Family Worship Church in Cotulla, which she had recently begun attending.

One of the ushers was a recovering drug addict. The pastor, Mark Linares, runs a barbecue stand outside his house. Ms. Vargas and her family walked in late, as Mr. Linares asked the audience to pray for a truck driver whose daughter-in-law was in a coma.

Everyone filed out of the red brick building, where there is a plaque by the front doors. Ms. Vargas and Ms. Salinas did not notice it. This was the old schoolhouse where President Johnson first saw extreme poverty in 1928. During the collection, the worshipers had passed around a basket. Ms. Vargas contributes when she can. This evening she had nothing to put in.