Still mourning the loss of a fellow representative, local U.S. senators and representatives are stepping up their personal security, though they may not be talking about it publicly.

After a deadly shooting Jan. 8 in Tucson, Ariz., that killed six, injured 14 and gravely wounded U.S. Rep. Gabrielle Giffords, many officials issued statements in support of Giffords' family but few came out strongly for or against additional security measures.

"I extend my deepest sympathies to the families of those who were gunned down in Arizona yesterday while participating in our democracy, and urge all Americans to pray for the victims who continue to fight for their lives," Sen. Saxby Chambliss, R-Georgia, said Thursday.

At this time, Chambliss' office won't comment further on security matters, noted spokeswoman Ashley Nelson.

Several representatives have said they are taking steps on their own to ensure better security, which could include staging town hall meetings in more secure locations such as fire stations.

But for other representatives, the shooting won't make a difference for security.

"Congressman Graves has not changed his normal routine other than to keep the victims of Saturday's tragic attack in his thoughts and prayers," said John Donnelly, communications director for U.S. Rep. Tom Graves, R-Ranger. "Security for official offices and events is being reviewed for any necessary updates, and the congressman will continue to review security recommendations offered by the House Sergeant at Arms."

Sen. Johnny Isakson, R-Georgia, shared a similar view Thursday.

"I am deeply saddened and disturbed by the senseless attack on Rep. Giffords, but we cannot let this stop democracy," he said. "I am elected by the citizens of Georgia and it is important for elected officials to remain accessible to our constituents. An additional security bubble would put up a barrier and make us less accessible. We can't let that happen."

House members left a private briefing with FBI and Capitol Police on Wednesday morning with explicit instructions to assign a liaison responsible for developing and maintaining closer relations with local authorities who can investigate complaints and provide security at public events in members' districts.

Several senior Republicans said it was too early to look at legislation either to broaden security protection for lawmakers or toughen criminal penalties and legal restrictions to deter future attacks.

"We are reviewing our security procedures in the district to ensure our staff is properly prepared for an emergency, but I do not anticipate making major security adjustments," Rep. Paul Broun, R-Athens, said Friday. "Officials have determined this was an isolated incident, and I will continue to make myself available to meet one-on-one with constituents in the 10th District of Georgia."