ASK any Republican presidential candidate, and they will tell you without hesitation: America's border with Mexico is as leaky as a sieve. Mitt Romney thinks all 1,969 miles (3,169km) of it must be fenced. Michele Bachmann wants a double fence. Rick Perry was pilloried for suggesting that in some rugged areas, more “aviation assets in the ground” might be better than fencing. Bemused by such talk, Barack Obama joked earlier this year that Republicans would not be happy until there was a moat full of alligators to keep illegal immigrants at bay. A few months later Herman Cain said there should be an electrified fence, with a charge strong enough to kill. He later explained that he too was joking, but would never apologise for standing up for America.

At the border itself, all this talk seems otherworldly. At a “processing centre” in El Paso, where the fingerprints of those caught crossing from Mexico illegally are taken and checked against various databases, there is precious little processing going on. Of the 20-odd workstations, only two are manned. The Border Patrol agents sitting at them chat idly to themselves. Just two detainees, their paperwork complete, sit timidly in the corner of an enormous holding cell. An adjacent cell for women stands empty. Next door, three more agents scan 25 screens relaying footage from video cameras along the border, looking for possible incursions. In some of the grainy pictures, scrubby and deserted patches of creosote and mesquite sway in a gentle wind; in others, herons peck at fish in the shallow trickle of the Rio Grande. Asked whether anything is going on, an agent replies, “it's really quiet today.”

It's quiet most days in the El Paso sector, as the Border Patrol dubs this 268-mile slice of the border. Back in 1993, agents arrested 285,781 people trying to enter America illegally. In those days, the holding cells in the processing centre, explains Scott Hayes, a Border Patrol agent, were full to bursting. In 2010, however, agents picked up only 12,251 illegal immigrants in the area—a 96% decline. Much the same is true of the border as a whole: last year's tally, of 447,731 arrests, is barely a quarter that of the peak year, 2000, when 1,643,679 people were intercepted. This year's figure will be under 350,000; a fifth of the peak.

The drop in arrests reflects not laxer enforcement, but stronger. There are over 17,000 Border Patrol agents on the border with Mexico, a fivefold increase over 1993. They patrol in cars and all-terrain vehicles, on bicycles and horses, in boats, planes and helicopters. When there are no agents around, cameras, reconnaissance drones and three different types of sensors—seismic, magnetic and infra-red—keep tabs on things. A third of the border is fenced, and most of the rest is in areas so remote or rugged as to make fences pointless or impractical. Some parts of the fence are 17 feet high, with metal plates extending ten feet below ground to prevent tunnelling. Along a two-mile stretch of the border just outside El Paso, five Border Patrol vehicles wait, ready to give chase should anyone manage to get past the fence. In the centre of town, where it is easiest for people to dash across from Ciudad Juárez on the other side and disappear in the busy streets, the entire border is floodlit. Elsewhere, agents have access to mobile lighting units, as well as hand-held infra-red cameras akin to night-vision goggles. There is even a special unit to chase hapless migrants through the city's storm drains. If anyone makes it past all these obstacles, there are checkpoints at the bus station, at railroad yards and on the main roads out of town, complete with dogs to sniff out stowaways. And there is more manpower and clever kit on the way. The budget for border enforcement and immigration has quadrupled over the past decade; the Border Patrol is still hiring. Agents used to be so outnumbered by the crowds flooding across that they could not give chase to all of them. They would return to their posts after arresting one group to find the tracks of several others who had crossed while they were away, Mr Hayes says. Nowadays plenty of agents respond to each breach. Those caught are not simply sent back across the border as they used to be: 90% suffer some sort of punishment—typically a few weeks in jail. What is more, the government has quietly started handing out more temporary visas for Mexican farm workers and the like, making it easier to enter legally. America's weak economy, and the falling birth rate in Mexico further reduce the incentives to cross. The Border Patrol will never manage to apprehend every last suspect, says Mr Hayes, but it is not that far off. Yet as Mr Obama suggested, the Republicans who have been bleating about the border are far from satisfied. They have hauled officials charged with policing it before Congress to berate their efforts. In states such as Arizona and Alabama, they have passed laws cracking down on illegal immigrants, on the grounds that the federal government has abdicated responsibility in that area. They refuse to discuss policies aimed at resolving the status of the 11m-odd illegal immigrants already in the country until they deem the border secure.

Mr Obama himself has succumbed to this mindset to a great extent. He has repeatedly requested increases in spending on Customs and Border Protection, which includes the Border Patrol, even as he has suggested cutting the budgets of other agencies. He has prolonged the deployment of some 1,200 National Guard troops along the border, to provide backup for the Border Patrol. The administration has boasted of deporting record numbers of illegal immigrants.

Yet there are some who question the entire premise of attempting to seal the border. Historically, says Doug Massey of Princeton University, the number of illegal immigrants from Mexico correlates most closely with economic growth in America and with the number of visas handed out, not with increased policing of the border. The whole thing is a colossal waste of money, he complains.