But interviews at shelters and passage points along both sides of the border this week, as well as an examination of recent immigration numbers, suggest that even with tightened restrictions on families, it’s going to be difficult for the president to stanch the flow.

Though it’s impossible to know yet whether the Trump administration’s “zero tolerance” crackdown on illegal border crossers will have a significant deterrent effect, one thing was clear this week at the Arizona-Mexico border: Many families — especially those from countries in Central America plagued by gang violence and ruined economies — are making the calculation that even separation or detention in the United States is better than the situation at home.

“Why would you undertake such a dangerous journey?” said Magdalena Escobedo, 32, who works at the migrant shelter here in Tucson, called Casa Alitas. “When you’ve got a gun to your head, people threatening to rape your daughter, extort your business, force your son to work for the cartels. What would you do?”