He sidestepped a question about whether more members should carry firearms, saying it is a personal choice.
"You never know when you might find yourself in that unfortunate situation," Chaffetz said. "It shook all of us. … She's someone you know and interact with. I have the same job."
Chaffetz also wondered aloud whether the incident could have been stopped or fewer people killed or injured had someone in the crowd in Arizona had a concealed weapon.
Paul Helmke, president of the Brady Campaign to Prevent Gun Violence, named in honor of President Ronald Reagan's press secretary, James Brady, who was shot during an assassination attempt, said people might have a different reaction to their public official if they thought he or she were carrying a weapon.
Helmke added regarding Chaffetz, "If he's afraid of people in his district, I certainly have no problem with him doing what he needs to protect himself. I just think he should do more to protect the American people."
Helmke added that Arizona is one of the states with the loosest gun regulation laws and that what actually stopped Saturday's shooter were bystanders tackling him when he had to reload. Had the shooter not been able to have a gun clip with more than 10 rounds, as was restricted under the lapsed assault rifle ban, fewer people could be injured or killed, he said.
Hatch staying vigilant • Sen. Orrin Hatch, R-Utah, said he has always tried to be vigilant in keeping his office and staff safe and will continue to do so but he doesn't plan any changes.
"We cannot allow tragedies to lessen the importance of the dialogue that elected officials have with the people we serve," Hatch said. "Listening and meeting with the people of Utah is essential and I will not allow [Saturday's] tragic events to alter the critical relationship I have with people from our state."
Lee speaks out • Also Sunday, Sen. Mike Lee, R-Utah, rejected the idea of boosting firearm regulations in the wake of the tragedy.
Lee, appearing on CNN's "State of the Union" Sunday program, said current laws already restrict who can own guns, and added that studies show areas with more firearms are safer.
"We have state and federal laws on the books that already prohibit citizens who have been deemed mentally ill from possessing firearms," Lee said on CNN. "I don't think we're going to lessen our way out of the risk [by adding more restrictions]. To the contrary, there is abundant research suggesting in cities where more people own guns, the crime rate, especially the murder rate, goes down."
Police have arrested Jared Loughner, 22, whom authorities say shot and killed six people and injured 14 others outside a Safeway grocery store in Tucson on Saturday morning.
Web videos allegedly posted by the Loughner have drawn questions about his mental state.
Asked after the program to clarify, Lee's spokeswoman Allyson Bell said Lee was not referring to a specific study on firearm ownership but that he has heard of multiple research reports showing diminished crime with increased gun ownership.
Lee, who became Utah's newest member of Congress last week, also cautioned Americans from trying to assign political motivation to the shooting of the Democratic congresswoman.
"This is a tragedy and I think it's disrespectful to the victims and their families for us to try to use it for short-term partisan political gain," Lee said. "I don't think we can tie this into anything other than a person who was either evil or mentally insane or a combination of both, and at this point it doesn't make any sense to turn it into a partisan political battle."
Like other members of Congress, though, Lee said the shooting wouldn't deter him from holding public events and he opposes the idea of adding more security restrictions for members.
"I don't think we should be adding any barrier between a member of Congress and [his or her] constituents," Lee said.