Washington (CNN) -- Federal firearms agents in Arizona cringed every time they heard of a shooting after letting waves of guns pass into the hands of Mexican drug gangs, some of those agents told a House committee Wednesday.

It was part of an operation aimed at tracking the flow of weapons across the U.S.-Mexican border, but the operation has come under intense criticism since the December killing of a U.S. Border Patrol officer. Operation Fast and Furious, as the program was known, was "a colossal failure of leadership," said Peter Forcelli, a supervisor at the Phoenix field office of the Bureau of Alcohol, Tobacco, Firearms and Explosives.

When U.S. Rep. Gabrielle Giffords was wounded and six others were killed in a January assassination attempt in Tucson, Forcelli said, an agency spokesman told him "that there was concern from the chain of command that the gun was hopefully not a Fast and Furious gun." Another agent, Lee Casa, said, "This happened time and time again."

"Every time there's a shooting, whether it was Mrs. Giffords or anybody, any time there is a shooting in the general Phoenix area or even in, you know, Arizona, we're fearful that it might be one of these firearms," Casa told the House Oversight and Government Reform Committee. The killings of three people connected with the U.S. consulate in Juarez, Mexico, caused similar anxiety, Casa said.

And a third agent, John Dodson, told lawmakers: "I cannot begin to think of how the risk of letting guns fall into the hands of known criminals could possibly advance any legitimate law enforcement interest. I hope the committee will receive a better explanation than I."

Operation Fast and Furious focused on following "straw purchasers," or people who legally bought weapons that were then transferred to criminals and destined for Mexico. But instead of intercepting the weapons when they switched hands, Operation Fast and Furious called for ATF agents to let the guns "walk" and wait for them to surface in Mexico, according to a committee report.

The idea was that once the weapons in Mexico were traced back to the straw purchasers, the entire arms smuggling network could be brought down. Instead, the report argues, letting the weapons slip into the wrong hands was a deadly miscalculation that resulted in preventable deaths, including that of Border Patrol Agent Brian Terry.

Terry was killed last year just north of the Mexican border in Arizona after he confronted a group of bandits believed to be preying on illegal immigrants. Two weapons found near the scene of the killing were traced to Fast and Furious.

"I was flabbergasted. I couldn't believe it at first," Terry's mother, Josephine, said of when she learned that the ATF may have let some of the guns used in the attack slip through its fingers. Terry's family said they want all those involved in his killing and who helped put the weapons in their hands to be prosecuted.

"We ask that if a government official made a wrong decision, that they admit their error and take responsibility for his or her actions," Robert Heyer, Terry's cousin and family spokesman, testified.

The committee's chairman, California Republican Rep. Darrell Issa, called the operation "felony stupid." As many as 2,000 semi-automatic rifles reached the hands of the cartels as a result, and Issa said the top two ATF officials were briefed the program regularly.

Assistant Attorney General Ronald Weich testified that the ATF never knowingly allowed the sale of assault weapons to straw purchasers, who then transported them into Mexico.

But Issa and other congressmen said the claim was deceiving. Although it is technically true that straw purchasers didn't cross any weapons into Mexico, they did transfer them to third parties who did, they said.

Issa also was upset over heavily redacted documents that his committee had received from the attorney general's office. Weich said his office was cooperating to the greatest extent possible, given concerns about disrupting the ongoing investigation. But Weich said he did not know or was not able to answer questions about who authorized the operation.

"The attorney general has said he wants to get to the bottom of it," he said.

Speaking before the committee, Sen. Charles Grassley, R-Iowa, said that the operation started with the flawed assumption that there was a large arms trafficking network that was operating.

"That kind of assumption can cause you to start with a conclusion and work backwards, looking for facts that fit the case. Until you figure out that you've got the cart before the horse, you're probably not going to get anywhere," he said.

Casa said ATF supervisors in Phoenix, where the project was based, brushed off several agents' concerns over letting guns go. And Dodson said that despite evidence that straw purchasers were giving their weapons to cartels, the agency went no further than to do some surveillance.

"Knowing all the while, just days after these purchases, the guns that we saw these individuals buy would begin turning up at crime scenes in the United States and Mexico, we still did nothing," he said.

Forcelli, also criticized the U.S. Attorney's Office in Arizona for what he described as a tendency not to prosecute arms trafficking cases, and said "toothless" laws against straw buyers made it difficult to recruit low-level operatives as witnesses.

"With these types of cases, for somebody to testify against members of a cartel where the alternative is seeing a probation officer once a month, they're going to opt toward not cooperating with the law enforcement authorities," he said.