Given the choice, Garcia said, she would rather have more agents patrolling the area. At least that would create some jobs, she added.
The region's lawmakers appear to agree. Three Democratic congressmen from the Texas border who support immigration reform have announced that they would not support any bill conditioned on the construction of more border fence.
"It doesn't do what proponents think it does," said Rep. Filemon Vela, of Brownsville, who resigned from the Congressional Hispanic Caucus in protest. "Building more fence makes no sense to me."
The fence's backers say it's a common-sense solution to keeping people from crossing the porous border.
The strip of land bisecting Garcia's La Paloma Ranch was eventually returned after the bi-national agency that monitors border treaties said the fence couldn't be built in a flood plain. But those objections were dropped last year, and the U.S. government has resumed planning for that fence.
The government is still in court with Texas landowners over the fencing built here last time. And yet, despite the existing barrier, the area leads the border in illegal-entry arrests.
Now the Senate's immigration bill calls for at least 700 miles of border fencing half of which already exists.
But even as Congress debates the issue, Customs and Border Protection has frustrated fence proponents and critics by failing to come up with any measurement of the fence's effectiveness. The agency told Congress' investigative arm last year that it needed three to five years to make a "credible assessment."
Farmers and others who live near the fence report seeing immigrants scale the 18-foot steel columns in seconds. And since the fence stands in segments across miles of open farmland, there's always the option of just walking around the barrier.
Homeland Security Secretary Janet Napolitano has said she supports the immigration reform bill passed by the Senate. But when asked about the fence, the agency said the barrier would be installed based on operational needs and that it was premature to discuss details.
David Aguilar, the Border Patrol's chief until he retired in February, said fencing is not appropriate everywhere or sufficient by itself.
"I'm afraid we do lose sight of last time. Everybody thought that the fence was the sole solution," Aguilar said.
Fencing, which costs on average of $3.9 million per mile, was part of the solution that helped the Border Patrol gain control of a stretch of border near San Diego.
Masses of people used to rush the border there, counting on agents' inability to catch everyone. Now the flow has slowed to a trickle.
As current Border Patrol Chief Michael Fisher described to a congressional committee in June, there's a stretch in Southern California that includes two layers of fencing with coils of razor wire on the second and an all-weather road for patrols. Towers provide 24-hour surveillance. Ground sensors alert agents if anyone tries to cross.
While most of the land for the border fence in California, Arizona and New Mexico was already in public hands, the opposite is true in Texas. The existing border fence already left hundreds of acres of farmland between the fence that runs in relatively straight lines and the winding Rio Grande. Condemnation cases filed in 2008 for the fence are still in court.
In June, a government lawyer told a federal judge in Brownsville that he planned to amend the original 2008 condemnation documents for one strip of land in the city to include more than 250 additional parties.
"We're a little bit behind the curve," Assistant U.S. Attorney Daniel Hu told the judge. "We've built the fence on land we actually haven't finished taking."
But while the rest of the Southwest border has seen fewer immigrant arrests, authorities in the Rio Grande Valley are busy.
It's unclear how much of the surge in arrests is what Aguilar termed a "deflection" from a tightened border at points west. More than half of the Border Patrol arrests in this sector are Central Americans, who have historically taken this more direct route into the U.S.
What is certain is that the arrests here are more than 50 percent higher through the first 10 months of the fiscal year than the same period last year. The Border Patrol sector is on pace to surpass longtime leader Tucson.
Still, for perspective, the 365,000 arrests at the border last year were a far cry from the high of 1.2 million in 2005. Most observers attribute the precipitous drop to the U.S. recession.
Los Ebanos, a community of about 300, is best known for having the only hand-pulled ferry on the border. Every day, the ferry carries three vehicles and a few people at a time across the river.
Garcia remembers when the Rio Grande overwhelmed its banks in 2010 and flooded most of her property, stopping just short of her home. She fears the fence would clog with debris, enhancing the flood risk. The U.S. side of the International Boundary and Water Commission shared that concern, but dropped those objections last year after a new round of hydraulic modeling suggested it would not be a significant obstruction.
Just up the street, Julie Garcia no relation to Aleida Garcia thinks the fence would run along the back of her father's property, about 100 feet from the riverbank. On a recent afternoon she traced the route immigrants take across her father's property and noted the large rusted propane tank they scramble up to clear a fence.
"I think it will be a great thing," said Garcia, who works in the oil fields. She knows that many of her neighbors don't want the fence. But, she said, "It's like the same thing at your house you build a fence to keep people out."