Mark Reed helped shape the strategy.
"We thought the mountains and the desert were going to be our friends in terms of this strategy. We thought that would deter entry through those places. And that those would be places that we would not have to worry about," says Reed.
Reed says officials figured the terrain was so difficult it was a deterrent but, he says, it turned out to be "our Achilles' heel."
"That's where the smugglers took them," he explains.
In a remote stretch of desert across from New Mexico, 60 Minutes met a smuggler and 11 young men preparing to enter the United States. The men rubbed garlic on their pants to ward off snakes. Then they crossed a three-foot barbed wire fence – each one carrying two gallons of water – nowhere near enough for a journey that could take five or six days. Last year, about a half million illegal migrants came from Mexico to live and work in the U.S., about twice as many as came before the border was fortified.
"It actually encouraged more people to enter the country because what we did is we took away the ability of a worker to come into the country and cross back and forth fairly freely. So they started bringing their families in and actually domiciling in the United States with their entire family because they knew they couldn't go back and forth," says Reed.
More than 20 percent of the deaths in the desert last year were women and children. The Border Patrol recorded 1.1 million arrests last year, but often it was the same people being arrested over and over again.
"I have caught the same group of people four times in one eight-hour shift," says T.J. Bonner, who is the head of the Border Patrol agents union.
But Bonner says the immigrants try to come another way after being turned back. "When I looked in the record log the next day, their names weren't there. So I can only assume that they got by us the fifth time," he says.
Fortified fences like the one in Nogales, Arizona, protect only about five percent of the U.S.-Mexican border.
Bonner thinks that the number of illegal migrants has actually gone up since the barrier went up. Does he think the millions spent on the fence were a waste of money?
"I think that's a fair assessment," says Bonner.
The U.S. government has spent about $20 billion on border control over the past 12 years. But Republican Congressman Tom Tancredo insists that is just not enough. He's sponsoring a bill that calls for more agents to remove illegal migrants where they work and to vastly increase border security.
"If you only put the fence for this five miles of border, people will go around it, naturally. You have to secure your borders!" says Rep. Tancredo.
He recommends sealing off the entire border, building fences. How much more should the government spend?
"Whatever it takes," Tancredo says. "Billions more. Billions more. Ed, why not? It is our job. It is what the federal government should be doing!"
The University of California's Wayne Cornelius, a national authority on immigration, predicted ten years ago that no matter what the government does to fortify the border, Mexican workers will still keep coming as long as there are jobs here for them.
"They can earn more in an hour of work in the United States than they could in an entire day in Mexico – if they had a job," says Cornelius.
The government says crossing the border through the desert is breaking the law, but Cornelius says the U.S. is sending a very mixed message.
"The message that we're sending them is if you can get past the obstacle course at the border, you're essentially home free. You have pretty much unrestricted access to our labor market and there are employers out there eager for your labor," he says.