Some members of Congress said they do not intend to ask for extra security at public events in their districts even after Saturday's shooting rampage in Arizona that killed six people and critically wounded Rep. Gabrielle Giffords (D-Ariz.).

Rep. Dean HellerDean Arthur HellerNevada becomes early Senate battleground Nevada governor Sisolak injured in car accident, released from hospital Democrats brace for tough election year in Nevada MORE (R-Nev.) told the Reno Gazette-Journal he's never felt threatened during his time in Congress and doesn't want any added security. 

"I wouldn't anticipate, unless this becomes more of a pattern, that anything would change at this point," Heller said.  

Freshman Rep. Chris Lee (R-N.Y.) said Sunday he won't take additional security precautions either, expressing concern that it would negatively affect his ability to communicate and interact with constituents. 

"I'm not, personally," Lee told a New York TV station when asked if he'll accept additional security. "You're here to represent people and you have to be accessible. We hope this is just a random act of violence, and it is so sad because she is a wonderful person." 

Rep. Reid RibbleReid James RibbleFormer lawmakers sign brief countering Trump's claims of executive privilege in Jan. 6 investigation The Memo: What now for anti-Trump Republicans? Influential Republicans threaten to form new party MORE (R-Wis.) said the same in an interview with a local TV station in his home state.

"There are deranged people that live in this world and, if anything, this is a reminder for all of us to be alert, to be aware of our surroundings and to pay as much attention to what's going on around us as we can," said Ribble.

Sen. Chuck GrassleyChuck GrassleyFormer Sen. Bob Dole dies at 98 Alarm grows over smash-and-grab robberies amid holiday season GOP blocks bill to expand gun background checks after Michigan school shooting MORE, the ranking Republican of the Senate Finance committee, and Rep. Steve King (R) also said they would decline additional security in response to the shooting.

King told The Des Moines Register he has received threats during his career, but not to the point he feels he needs additional protection.

“So if it means I always have to have a security detail, I’m probably going to be the guy that figures out how to escape my security detail and deal with real people,” King said.

Grassley stressed the importance of being able to talk directly to the public.

“I don’t know how I can change my procedure at all from the standpoint of just going on and doing what we’ve been doing,” Grassley said.

Still, some other members were quick to call for additional security measures. 

Rep. Raul Grijalva (D-Ariz.), who was the subject of death threats last year, said he intends to "insist on more security ... [so] we can make sure this doesn't happen again." 

Rep. Doug Lamborn (R-Colo.) said he intends to ask local authorities to provide additional security at town hall meetings planned for his district. He told a Colorado TV station his office will ask for added security "wherever I'm having the town hall meeting" in order to "reassure the public that we do have security."  

Also on Sunday, a top House Democrat said Congress might need to "beef up the funding" for the offices of individual members — money they could use to arrange added security for events in their home districts. 

Rep. James Clyburn (D-S.C.) made the comments on Fox News Sunday, where he also called for special treatment for members by the Transportation Security Administration at the nation's airports.

—Bob Cusack, Sean J. Miller and Daniel Strauss contributed.