Border Patrol officials emphasize they are doing more than ever. In the 1990s, agents here recall, they did not have a budget to keep their gas tanks full. Now staffing levels in the sector have more than tripled, to about 2,500 agents. Additional intelligence comes from drones and helicopters, along with cameras set up by the state to track wildlife.

The Border Patrol has also received help from the National Guard and about 100 members of a Border Patrol mobile response team that was created a few years ago to move along with smuggling patterns.

In many ways, the dynamic response reflects a broader evolution in border policing. In the 1990s and after 2006, when Congress set aside $2 billion to build border fences, the approach focused on static technology. San Diego was the model, with its three layers of fence and cameras atop poles 85 feet tall. But immigrants soon adapted and crossed elsewhere. So, as migration moved to Arizona and then to Texas, officials began to focus on mobility. Rosendo Hinojosa, the chief of the Rio Grande Valley sector of the Border Patrol, says he now wishes he could move the permanent cameras, which were set up east of McAllen in 2001, to busier areas.

A calm, commanding man built like an offensive lineman, he praised residents for getting more involved, noting that law enforcement now regularly receives tips about stash houses where immigrants are kept before moving farther north. But during a flight over his area in a small plane, the dizzying challenge of border security twisted and turned with the Rio Grande.

Chief Hinojosa pointed to several spots that were impossible to fence and hard to defend. Flying west from McAllen, he pointed to sugar cane fields just a few feet from the river — giving immigrants an immediate place to hide — and to a sharp riverbend near where Ms. Ochoa lives, noting it is where drugs and people often come ashore because of boat ramps easily reachable by car. Over Mr. Zamora’s small blue house, Chief Hinojosa highlighted the proximity to major roads. “If we don’t have a persistent presence there, then they’re across in 30 seconds and on a highway,” he said. (When this reporter saw the four men cross, it was just minutes after a Border Patrol shift change.)

Mr. Bonner, the former customs commissioner, whose career has included stints as a judge and the head of the Drug Enforcement Administration, said the best way to measure border security involved comparing the number of people who are caught with those who crossed successfully. The senators proposing an immigration overhaul might also welcome the clarity of such a statistic, given that they have not yet agreed upon how to measure border security.

But that figure may be impossible to know. Though the Border Patrol tracks detected migrants who got away, and those who turned back to Mexico or were apprehended, the agency’s nine sectors use different procedures for classifying such occurrences, a flaw the Government Accountability Office identified in a December report.