President Obama’s decision last year to send 1,200 National Guard troops to the U.S.-Mexico border may have been smart politics, but a growing number of skeptics say the deployment is an expensive and inefficient mission that has made little difference in homeland security.

Critics of the deployment include budget hawks, who say it is a waste of money, and residents here along the border, who say they are tired of seeing armed troops in their back yard.

State Department officials worry that the domestic use of U.S. troops increases the perception that the border is militarized, while Chamber of Commerce boosters say the National Guard presence sends the message that the American side of the border is a dangerous place, though it is not. Crime statistics show that the border is one of the safer regions in the country.

Most of the criticism of the deployment focuses on its costs and benefits. The 1,200 National Guard troops have helped Border Patrol agents apprehend 25,514 illegal immigrants at a cost of $160 million — or $6,271 for each person caught.

“As a mayor, I am not going to say we don’t want more security. But as a taxpayer? I would say something different,” said John David Franz, mayor of Hidalgo, in Texas’s Rio Grande Valley.

Proponents of the mission stress that the guardsmen serve as a deterrent to drug smugglers and illegal immigrants — a role that is impossible to measure in dollars.

Under pressure from governors in the southwestern border states, Obama ordered the deployment, dubbed Operation Phalanx, in July 2010 amid a federal showdown in Arizona over a controversial new law targeting illegal immigrants. Members of Congress — Democrats and Republicans alike — also pushed the president to deploy the Guard, saying they feared that spillover violence from Mexican drug cartels would overwhelm the 2,000-mile frontier.

While citizens might imagine the National Guard patrolling the muddy cane breaks along the Rio Grande in search of drug cartel incursions, many of the troops instead serve as stationary observers, a kind of neighborhood watch with M-16s, often perched 30 feet in the air in skyboxes, portable watchtowers the size of phone booths.

Other troops work the telephones and computers in back offices, as clerks in camouflage.

According to rules of engagement set by the Pentagon, Guard troops are not allowed to pursue, confront or detain suspects, including illegal immigrants, or investigate crimes, make arrests, stop and search vehicles, or seize drugs. Nor do they check Mexico-bound vehicles for bulk cash or smuggled weapons headed to the drug cartels.

“We are the eyes and ears, mainly. We do not have a law enforcement role,” said Maj. Gen. Hugo E. Salazar, head of the Arizona National Guard, who said that his 560 soldiers in Arizona mostly act as an “entry identification team,” watching the border fence.

When the Guard troops spot suspicious activity, they radio Border Patrol agents, who make the apprehensions and drug seizures.

“We don’t chase anybody,” Salazar said.

‘Staring at a fence’

Critics of the deployment say the Guard is doing less than ever. Not only is its role limited, but there are far fewer soldiers than the governors wanted. Under the George W. Bush administration’s Operation Jump Start, more than 6,000 troops were sent to the border between 2006 and 2008, at a cost of $1.2 billion, and they dedicated themselves to building miles of fence and roads.

“This deployment is different. The public perception along the border is that if they see the National Guard at all, they are sitting on a hilltop in lawn chairs, with pair of binoculars, staring at a fence,” said Adam Isacson, an expert in regional security at the Washington Office on Latin America, a think tank.

“With all due respect, the job of the National Guard is not being a Border Patrol agent or customs inspector,” said Monica Weisberg-Stewart, the owner of Gilberto’s Discount House in downtown McAllen, Tex., and chair of the Texas Border Coalition’s security committee.

“We don’t want to see them in McAllen,” she said. “No offense.”

Other residents are more positive. “There aren’t that many of them here, but I think they serve as one more deterrent for the bad guys,” said Hector Ruiz, an air-conditioning repairman in McAllen.

Because the Pentagon is concerned about force protection, the National Guard troops must always work in pairs, while Border Patrol agents often operate alone.

In an August report on the costs and benefits of an increased role for the Defense Department along the U.S.-Mexico border, the Government Accountability Office told Congress that it takes three people to do the job of one: two Guard soldiers to spot an illegal crosser and one federal agent to catch him.

“We pointed out that it is not a very efficient use of manpower,” said Davi D’Agostino, a director at the GAO.

Though there has been a spectacular surge in gruesome killings in Mexico, where more than 43,000 have died in drug violence since late 2006, there is little evidence of spillover into the United States.

The National Guard is working the border at a time when arrests of illegal crossers have fallen to historic lows and the number of Border Patrol agents has soared.

There are now 18,152 Border Patrol agents stationed along the southwestern border, up from 9,100 in 2001. Apprehensions of illegal crossers have fallen by two-thirds, from a high of 1.6 million in 2000 to 447,731 last year. This year’s tally is expected to be lower still, reaching levels not seen since the early 1970s.

‘Is this just politics?’

Border Patrol officials concede that their agents struggle with boredom and to stay awake.

“At a time when apprehensions have plummeted, it is increasingly hard to justify the Guard deployment,” said Doris Meissner, a former commissioner of the U.S. Immigration and Naturalization Service and now a director at the Migration Policy Institute. “With such an enormous investment in our Border Patrol, it is a valid question to ask: Is this just politics?”

Proponents of the deployment point out that the National Guard is credited with helping law enforcement seize 83,629 pounds of marijuana in the past 16 months. That is about 2.6 percent of the tons of pot seized each year along the southwestern border.

During its deployment, the Guard has not assisted in any major seizures of heroin, cocaine or methamphetamine, nor has it been credited with helping take down cartel “kill teams,” cross-border kidnappers or major trafficking networks, according to information provided by the Customs and Border Protection agency.

“I would thank them warmly for their valuable service, send them home and invest the millions saved in better inspections at the ports, beefing up international efforts to target cartel leaders and getting the Treasury Department . . . into action” to go after cartel money launderers, said Terry Goddard, a former Arizona attorney general.

This summer, at the urging of congressional leaders, Obama extended the National Guard deployment until the end of 2011. Most political observers expect the administration to continue the mission through the 2012 election year.