After the Border Patrol began to release migrants in McAllen early last week, hundreds came to the refuge that community volunteers and city officials hastily set up in the Sacred Heart Catholic Church.

In Washington, the increase in illegal immigration has provoked a new argument between the White House and Republicans. Obama administration officials insist that factors in Central America, including poverty and criminal violence, are driving the migrants. Republicans blame lax enforcement by the administration. Representative Robert W. Goodlatte, Republican of Virginia and chairman of the House Judiciary Committee, will hold a hearing next week on what he described as “an administration-made disaster.”

At the church, some women said the talk about an entry permit, which has intensified in the last two months, had prompted them to set out on the risk-filled journey across Mexico. But the women said they were moved mainly by desperate worries about their children, with poverty unrelenting in their countries and warring street gangs expanding their control.

The Central American migration has created unusual difficulties in the Rio Grande Valley for border authorities, who must follow differing rules for unaccompanied minors; for migrants who are not from Mexico; and for women who have children or are pregnant.

Since October more than 47,000 unaccompanied youths have been apprehended along the Southwest border, and border officials estimate that number may double by the end of this year. The Border Patrol is required to transfer unaccompanied youths within 72 hours to a refugee agency in the Department of Health and Human Services, which runs shelters for them and works to locate parents or guardians in the United States. Federal emergency officials have opened new shelters for the children at three military bases and are coordinating food, medical care and legal assistance.

From the shelters, youths are sent to live with parents or relatives here or to longer-term foster care if they have no family here and have grounds to fight deportation. Otherwise, they face deportation.

For women with children, the Obama administration has a longstanding policy of seeking separate, family-friendly detention centers or releasing them, often without bond.