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"Look," Mr. Zamora said early one recent morning, "here they come now." He pointed toward his neighbor's yard, where a young man in a dark sweatshirt and white sneakers sprinted toward the road, his breath visible in the winter dawn. Three others followed, rushing into a white sedan that arrived at the exact moment their feet hit the pavement.

"I don't know how the government can stop it," Mr. Zamora said, watching the car drive away. "It's impossible to stop the traffic. You definitely can't stop it with laws or walls."

The challenge has tied Congress in knots for decades, and as lawmakers in Washington pursue a sweeping overhaul of immigration, the country is once again debating what to do about border security.

A bipartisan group of senators has agreed in principle to lay out a path to American citizenship for an estimated 11 million immigrants in the United States illegally, but only after quantifiable progress is made on border security, raising thorny questions: What does a secure border mean exactly? How should it be measured? And what expectations are reasonable given the cost, the inherent challenges of the terrain and the flood of traffic crossing legally each year in the name of tourism and trade?

Some Republicans argue that the southern border remains dangerously porous and inadequately defended by the federal government. Obama administration officials, insisting there is no reason for delaying plans to move millions of people toward citizenship, counter that the border is already safer and more secure than ever. They say record increases in drug seizures, staffing and technology have greatly suppressed illegal traffic, driving down border apprehensions to around 365,000 in 2012, a decline of 78 percent since 2000.

Indeed, by every indicator, illegal migration into the United States has fallen tremendously — in part because of stricter immigration enforcement — and has held steady at lower levels for several years.

But all camps leave a lot out of the discussion. Visits to more than a half-dozen border locations over the past two years show that the levels of control vary significantly along the line in ways that Congress and the White House have yet to fully acknowledge.

Many areas that used to be popular crossing points have experienced undeniable improvements. Migrant shelters across from El Paso are now often empty. A generation after San Diego was overrun with thousands of immigrants openly rushing into the city every day, experts, Border Patrol agents and deportees in Tijuana, Mexico, all say that the chances of reaching Southern California are remote, with odds of success at 1 in 10, or worse.

Other sections of the border have seen less progress. Here in the Rio Grande Valley, crossings by the dozen still occur regularly, with relative ease, despite noticeable increases in the Border Patrol's capabilities. The governmentwide spending cuts that went into effect on Friday could lead to even greater vulnerability.

And even before the budget battles, politics undermined effectiveness. Population centers like San Diego have held on to more resources; there are 80 Border Patrol pilots in the San Diego sector and only 15 in the Rio Grande Valley, where there is more migrant traffic — a sign of inefficiency that the Obama administration glosses over with national staffing figures.

With a similar degree of omission, Republicans demanding more fencing rarely mention that here, along hundreds of miles of a twisting river border with farms and parks on its edge, such an approach would mean seizing private property, damaging the environment and spending billions.

It is increasingly clear to those who live along the boundary with Mexico — or who try to protect it — that there is no such thing as a completely secure border, just as there are no cities without crime. Even in areas with towering walls and drones or helicopters overhead, border security can be breached.

The international divide is not a line or a series of doors to be locked and guarded, they argue. It is more like a 2,000-mile shoreline with ever-changing currents of migration, legitimate trade and smuggler tactics. The challenge evolves season to season. In Texas, where the border moves with the flooding of the Rio Grande, smugglers have started using fake Halliburton trucks to drive through areas where the company services oil fields. In San Diego, a few hundred migrants a year now arrive by boat, while the imposing fences that cost $16 million per mile are regularly overcome with ladders rented out for $35 a climb.

"The U.S. border with Mexico is better controlled than at any time in our history," said Robert C. Bonner, who served under President George W. Bush as the commissioner of the United States Customs and Border Protection. But, he said, there is a lack of understanding among policy makers and the public about the challenge. "The terrain can be quite different depending on what part of the border you are talking about, and there are different ways, different tactics really, that need to be brought into play," he said. "And this requires almost mile-by-mile analysis."

Crossing Points

Suly Ochoa, 56, a home health care aide whose peach-color home sits along the border wall in Granjeno, Tex., says that what she wants from the border policy is simple, "It needs to be smarter."

Like many of her neighbors in this town of 303, which was founded on Spanish land grants in 1767, she and her family have seen immigrants crossing through the area's mesquite trees and tall grass for decades.

They have often helped the most desperate, calling ambulances for children or pregnant women. But residents have become increasingly concerned about security, as Mexican drug gangs seized the business of moving people and narcotics. Crime in the larger area of McAllen, Tex., while low, now occasionally includes what appear to be targeted killings.

Ms. Ochoa, a no-nonsense woman who grew up here, said she and many others in Granjeno had hoped the $20 million border wall — a 1.7-mile stretch of concrete and dirt, rising 18 feet — would help them feel safer. Now, a few years after completion, it looks to her more like a waste. "It's not working at all," she said, standing near the wall. "To me, it's money down the drain."

Part of the problem is that the fences and walls cover a limited area here in the Rio Grande Valley sector — just under 54 miles staking out a relatively straight boundary near the 316 curving miles of river border. And even within the fenced area, because of the riverfront farms and parks, there are several gated openings. The road in front of Ms. Ochoa's house leads over the wall (which also serves as a levee), giving the authorities and smugglers access to the Rio Grande.

Border Patrol officials say that, even with the breaks, the barriers help by funneling illicit traffic into areas where crossers can be more easily caught. But residents say the system often fails. Ms. Ochoa says she sees drug loads at least once a week — usually large pickup trucks with bales of marijuana in the back barely covered with a tarp. Immigrant crossings occur almost every night, usually in groups of 10 to 20 people rushing by, sounding to many like stampeding horses.

One of Ms. Ochoa's neighbors, Gloria Garza, 56, says she sleeps with the television on to drown out the noise. "You feel like they're invading your privacy," she said. "It's not that you have anything against them. It's just a question of who's in the bunch."

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.

The numbers are useful for showing trends. The Yuma sector in Arizona, for instance, has seen the biggest improvement: in 2011, only 6 percent of migrants managed to get away from border agents after being detected, down from 36 percent in 2006. The rest either turned back toward Mexico or were caught. The Rio Grande Valley sector has also seen progress, with 29 percent getting away in 2011, down from 44 percent in 2006, though that is still poor by national standards. Only the Big Bend sector, east of El Paso, which is more isolated and sees far less traffic, had a higher rate of getaways.

Even so, the statistics are woefully incomplete because the Border Patrol agents count only the immigrants they detect, not the countless others who cross without anyone noticing.

The four men crossing by Mr. Zamora's home were not part of the tally. Nor is there a count of those who have successfully used stolen documents, mingling in with the 350 million people who legally cross the border every year. Nor, officials acknowledge, can they keep up with all the new ways smugglers manage to avoid detection. In Texas, it is not just Halliburton trucks that they mock up. They have also impersonated shipping companies, including FedEx.

Rising Costs and Risks

Criminal organizations dominate Reynosa, the Mexican city across the border from McAllen , and they have made smuggling along this section of the border a sophisticated monopoly. The Gulf Cartel controls access to the river (called the Río Bravo in Mexico) and will beat or kill anyone who tries to cross without paying.

"Over there, they respect your life," said a Honduran man at a migrant shelter in Reynosa, referring to the United States. "On this side, they don't."

He and several other men said they knew it was possible to get across, though, if they paid $2,500. The cost to be guided across has gone up significantly over the past decade, according to surveys and Border Patrol officials, who say this shows they are making the journey more difficult. But the prices (around $7,000 for the trip from Central America, with $4,000 up front) are still being paid, often by relatives in the United States. And even apprehensions and seizures do not always amount to clear victories.

On weekends, smugglers often rush the border from several points, agents and immigrants said, which means more drugs and immigrants are caught — and more get through. Smugglers have also become masters of decoys and delays. Ms. Ochoa said she had seen smaller cars pulled over, followed by large trucks that slip by while the authorities are tied up.

Similarly, the night after Chief Hinojosa highlighted the sector's hot spots, dozens of agents spent several hours tracking a group of migrants who had crossed the river between Ms. Ochoa's and Mr. Zamora's small towns. The migrants had tripped a ground sensor, then a drone and a helicopter — equipped with heat-detecting cameras — confirmed that there were people making their way north through the brush in the flood plain. Slowly, the teams moved in, on horses, in trucks and with A.T.V.'s.

It was an impressive display that yielded a mixed result. A handful of officers walked three men up from the brush, along with two teenage boys and a tearful young woman with a pink cellphone. All but one came from Central America and would soon be sent back.

But that was just part of the group. Eight others had gotten away, the agents said, along with the two guides, who appeared to have fled back across the river into Mexico.

Less than an hour earlier, it was much the same with a shipment of drugs. Two men carrying backpacks ran through a gap in the border fence. The cocaine they were carrying ended up seized, but the smugglers escaped. They had thrown down homemade spikes — nails welded together to pop the tires of Border Patrol trucks — and that was all they needed. Despite dozens of agents in the area, a fence and surveillance overhead, they were able to slip away by blending into McAllen.

"If they weren't getting in," said one border official who works at ports of entry, "they wouldn't be trying."

The next morning, Mr. Zamora saw the four migrants cross in front of him. Chief Hinojosa said border crossers are often caught deeper into Texas, at the checkpoint on Highway 83 heading out of the valley.

But Mr. Zamora seemed ambivalent, going back and forth between annoyance and resignation. Leaning on a steel pole for support, his 77 years looking more like 88, he said that as long as immigrants could find work — as long as the incentive system far from the border stayed the same — people would come. He knew it because it was his own experience. Though legal now, as a young boy more than 60 years ago, he swam across the same river to pursue the American dream.