The current surge has overwhelmed U.S. Customs and Border Protection. Designed mainly to handle single adults — traditionally, Mexican men seeking work — the agency’s resources and remote outposts are ill-equipped to deal with children and families, some of whom arrive in poor health. Administration officials have taken some useful steps to address the crisis, mainly by revamping and expanding medical care, deploying additional interpreters and adding a processing center in El Paso.

Nonetheless, it remains the case that the migration records being broken involve the composition of migrants (more families, who now constitute 60 percent of arrests at the southern border), not the overall number of arrests by Border Patrol agents, which remains way below historical levels. The president seeks construction of 200 additional miles of barriers, and even if it could be completed within a year or two, which is improbable, it would do little to impede the flow of asylum seekers, who are permitted by law and international treaty to seek refuge in the United States.

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The unintended (but highly conceivable) consequences of building more miles of border barrier include pushing those asylum seekers to cross in ever more isolated spots. One reason so many families are now turning up in remote places is that they are being turned away from legal entry points by officials citing limited capacity. The lesson is that migrant flows are like a balloon: Squeezed in one place, they will grow in another.

That raises the question of Mr. Trump’s efforts to curtail development assistance and other forms of foreign aid to migrant-producing countries. Lashing out at a new caravan of migrants last fall, he threatened to cut off funding for Guatemala, Honduras and El Salvador if their governments “allow their citizens” to set off for the United States. In fact, his administration had already taken steps to trim U.S. aid for the crime-ridden, impoverished countries of the so-called Northern Triangle. For example, the $69 million the administration requested for development aid in the current fiscal year for Guatemala — a major source of the most recent migrants — is the smallest ask in a decade.

According to the Congressional Research Service, the administration’s aid request in the fiscal year that ended last fall “would have reduced funding for every country and regional program in Latin America and the Caribbean.” In the event, Congress appropriated more than the administration asked for but less than in previous years. But Mr. Trump’s instinct to punish, not help, countries whose people leave is the wrong prescription for a mounting problem at the border.