The stunning White House security breach in which an intruder led officers on a chase through the residence earlier this month has raised a basic question from lawmakers and others -- why didn't the officers use lethal force?

The suspect, Omar Gonzalez, allegedly was carrying a knife at the time and had had encounters with law enforcement before. Secret Service Director Julia Pierson, speaking before a House committee on Tuesday, even testified that a couple officers recognized him just before he jumped the eight-foot White House fence and barreled toward the building.

Further, a source familiar with the investigation confirmed to Fox News that the intruder was only stopped when an off-duty Secret Service official -- part of the sniper team typically assigned to the White House roof -- tackled him. The detail raises new questions about why the on-duty team failed to catch him.

"Don’t let somebody get close to the president. Don’t let somebody get close to his family. Don’t let them get into the White House. Ever," Rep. Jason Chaffetz, R-Utah, told Pierson at Tuesday's hearing.

The lawmaker added: "And if they have to take action that’s lethal, I will have their back."

But the question of when Secret Service officers should open fire on intruders is a complicated one, and Chaffetz faced plenty of push-back at Tuesday's hearing.

In this case, the first family was not home. Some suggested the agents were right not to fire at Gonzalez.

"There are guests in the White House," said Rep. Gerry Connolly, D-Va. "It is a busy and bustling place, and the idea we're gonna have a shootout on the White House grounds seems to me a last resort, not a first resort."

Pierson admitted Tuesday that protocols in place to protect the White House were not "properly executed" in the Sept. 19 incident. She made clear that officers can use "lethal force" to stop a White House intruder -- but at the same time said the agency showed restraint by not shooting Gonzalez.

The explanation given in media accounts for why Secret Service officers did not open fire was, in part, that they saw he didn't have weapons in his hands and wasn't wearing the kind of clothing that could hide a lot of explosives. But, as the affidavit filed in federal court later revealed, the suspect was carrying a knife with a three-and-a-half-inch blade.

"I hate to even imagine what could have happened if Gonzalez had been carrying a gun instead of a knife when he burst inside the White House," Rep. Ellijah Cummings, D-Md., said. "That possibility is extremely unsettling."

Jeffrey A. Engel, director of Southern Methodist University’s Center for Presidential History and an expert in presidential security, suggested restraint is a virtue in these situations.

Engel said had the officers shot and killed Gonzalez it “would have been a horrible, horrible story” and said that “the suggestion that we should just shoot people who jump the fence is cold-hearted.”

During last week’s security screw-up, at least five layers of protection to secure the perimeter around the White House failed.

The first miss came at the North Gate, where a team of plainclothes officers didn’t see the intruder climb an eight-foot fence.

Gonzalez, who also had a hatchet and ammunition in his car, allegedly made it past a guard booth officer, the SWAT team and a K-9 unit. He entered an unlocked door, made it past a Secret Service officer and got all the way to the East Room of the White House before he was apprehended.

After the incident, the Secret Service released a press release stating that while “the officers showed tremendous restraint and discipline in dealing with this subject, the location of Gonzalez’s arrest is not acceptable.”

Chaffetz says that’s not good enough.

“Tremendous restraint is not what we’re looking for … the message should be overwhelming force,” he said.

But Engel said there are several cases of teens, tourists and sometimes even toddlers slipping past the initial perimeter and that it’s up to the agents to exercise judgment in these cases. Engel said if a suspect has a visible firearm or is carrying a satchel – which often indicates explosives – agents would most likely have used more force.

Gonzalez had neither.

Though the first family was not home, Engel said protocols to guard the White House are the same regardless of whether the president is there. Ultimately, he said that had Gonzalez been running toward the president or a member of the first family, he “wouldn’t have made it 10 feet."

Others see it differently.

Dan Bongino, a former Secret Service member who is running for Congress, blames the White House security breach on political pressure on the agency to “maintain optics.”

“It was only a matter of time given the jurisdictional mess in front of the White House and the constant pressure on the Secret Service to maintain optics,” Bongino told Fox News on Tuesday. He added, “We can go on and on about over-bureaucratic government but it has very real consequences as we’re seeing now. Now, I’m not apologizing for them, this was a security failure.”

Fox News' Ed Henry contributed to this report.