Washington (CNN) -- For Rep. Jackie Speier, the vicious attack on her colleague Gabrielle Giffords and others in Tucson, Arizona, brought back a chilling memory of when she faced an attempt on her life.
In November 1978, Speier and her boss, Democratic Rep. Leo Ryan, went to Jonestown, Guyana, to investigate Rev. Jim Jones' People's Temple, which had members from Ryan's California district.
As he was escorting some members of the church to his airplane to return to the United States, Ryan was was shot and killed and Speier was seriously wounded.
At the same time, members of the church were committing mass suicide in what became known as the Jonestown Massacre.
The news of Giffords' shooting revived those memories, Speier said.
"I certainly had all those emotions and all those flashbacks," Speier, a Democrat from California, told CNN on Monday. "My stomach is still churning because I know exactly what Gabby is going through right now."
The shootout, though, did not discourage Speier from entering public service, because "you can't take the acts of single individuals and somehow multiply that into that's what the American people were all about."
Speier said she is not going to change the way she operates -- engaging her constituents and offering full access.
"It is important for us to be able to meet and greet the people that we serve. And if we start having police presence everywhere we go, it's going to create a chilling effect on discourse and it creates an incredible assault on the democratic process."
Speier pointed to the contentious town hall meetings in 2009 over the health care overhaul bill before Congress, in which angry rhetoric and near-violence captured national attention. She said local police attended virtually all her town halls -- a decision made by authorities "because they wanted to maintain calm."
Her message to the public and media: Lower the incendiary rhetoric.
Rep. Jason Chaffetz agreed, saying more needs to be done to tone down the heated comments. The Utah Republican said that not only does he have a concealed weapon license -- legal in his state -- but that he "may do it (carry it) more regularly now" after Giffords' attack.
Congress should consider using the U.S. Marshals Service, which protects federal judges, to provide security for lawmakers in their districts, he added.
Saturday's shooting has also elevated awareness at the Capitol.
House Sergeant-at-arms Bill Livingood, in an e-mail, told members that they should contact him if they hold public events, and ask local police to attend.
"I strongly urge Members and staff to be continuously aware of their surroundings and to immediately report circumstances that appear suspicious to your local law enforcement agency and then to the U.S. Capitol Police Threat Assessment Section," he wrote. "It is essential that each District Office establish communication with local law enforcement. The local agency should be informed of your District Office address and the Member's residential address."
Sources say lawmakers will receive a more in-depth briefing Wednesday from Capitol Police, the sergeant-at-arms and the FBI.
Arizona Republican Rep. Jeff Flake was one of 800 people participating on Sunday in a rare bipartisan conference call with members of Congress, their families and staffs.
"It was to hear what we can do and hear what members are advised to do in terms of if you don't have a relationship or current contact information with your local law enforcement, be it county or city or (state police)," Flake told The Arizona Republic. "If there is a concern at a particular event that you are having, that if this isn't something that Capitol police or federal police can be involved in," then local law enforcement should be notified.
Flake told the paper that his office already works with local police, who phoned his office during the health care debates to offer to provide security.
Rep. Debbie Wasserman Schultz, D-Florida, said the Arizona shooting "needs to be a wake-up call for members who have treated their own personal security in a cavalier way."
"Not a cavalry of officers, but at least a show of law enforcement so that we can make sure my staff is protected," she said on NBC's "Meet the Press" on Sunday.
Wasserman Schultz added that she always has local police with her at town hall events in her district.
With Congress looking to make cuts to legislative budgets, Rep. Jim Clyburn, D-South Carolina, said that security funding shouldn't be one of them.
"We ought to look at whether or not we may need to beef up the funding ... so that Congress people can work with their state and local law enforcement officers," he told Fox News.
CNN's Dana Bash and Deirdre Walsh contributed to this report.