At the relief center on Wednesday, Lilian Morales Gonzalez, 22, tried to soothe her crying 2-month-old baby, a statue of Jesus behind her. She came from Guatemala — “so my son can grow up with his father,” she said — and was apprehended on Monday morning. She said Mr. Trump and his policies had no effect on her decision.

Ismelda Cruz, 28, also came from Guatemala. She, her husband and 7-year-old daughter crossed the Rio Grande at Reynosa, Mexico, fleeing the criminals she said were trying to recruit her husband. Asked if the presence of National Guard troops would deter people from making the journey from Guatemala, Ms. Cruz replied, “They’re always going to find a way through.”

Migrants who were recently apprehended, longtime residents and local officials in McAllen and other cities in the Rio Grande Valley said that with or without the National Guard, and with or without the White House’s increasingly anti-immigrant rhetoric, people would keep crossing. They worry that a deployment of troops would hurt the region’s economy and add to the inaccurate perception that Texas’ border cities were unsafe.

“We’ll get the bad publicity,” said Tony Martinez, the mayor of Brownsville, an hour’s drive to the east. “Nobody is sitting around here locking their doors and taping up their windows. It’s not a matter of security. Immigrants don’t want to migrate. They have to. This charade that Washington, or Trump more particularly, is imposing on the border is nothing more than empty rhetoric.”

A show of military force on the border in this part of Texas would be nothing new.

The Texas Republicans who lead state government have spent hundreds of millions of dollars on increasing border security, deploying heavily armed river patrol boats, purchasing a high-tech surveillance airplane and posting state troopers in the highway medians near the border, and previous United States administrations have on occasion dispatched National Guard units. In 2014, former Gov. Rick Perry ordered 1,000 National Guard troops to the border, in a state-ordered mobilization that Gov. Greg Abbott continued after he took office in 2015.