"Public service is a high honor, but these tragic events remind us that all of us in our roles in service to our fellow citizens comes with a risk," Boehner said in Ohio. "This inhuman act should not and will not deter us from our calling to represent our constituents and to fulfill our oaths of office. No act, no matter how heinous, must be allowed to stop us from our duty."
Boehner and Pelosi, as leaders, both rate round-the-clock protection from the Capitol Police.
Most lawmakers, like Giffords, do not get special police protection.
Attacks on members of Congress are rare. The last federal lawmaker to die violently was Rep. Leo Ryan, D-Calif., who was shot and killed in Guyana in 1978 while on a trip investigating the Jonestown cult settlement there.
Rep. Jackie Speier, D-Calif., was with Ryan as an aide in 1978 and was shot five times. She survived and now represents the same Northern California district that Ryan did.
She told ABC News Saturday she's adamant, at least for her part, that security for members of congress not be increased at home.
"I certainly don't want to have to be required to have a police presence," she said. "If that's the case, then it's time for me to no longer be a congressmember."
It is not clear what motivated the shooter in Arizona.
Giffords' Arizona district office was vandalized after her vote for the health care bill in March 2010, but there are no references to that law in the rambling posts on the shooting suspect's Myspace and YouTube pages.
Her seat was one of the most competitive in the country and she barely defeated Tea Party favorite Jim Kelly last November.
Despite the lack of an apparent correlation between Giffords' shooting and any specific political vote or belief, some Democrats said they were taking special precautions after the shooting.
"We have taken appropriate steps in light of the tragedy today in Arizona," Justin Ohlemiller, district director for Rep. Andre Carson, D-Ind., told The Associated Press.
Lawmakers are left to their own devices for security at home. A staffer to Sen. Jim Webb, D-Virginia, was arrested in 2007 when he accidentally tried to take the senator's gun into a Capitol Hill Office building.
At the time, Webb said lawmakers have to be careful.
"I'm a strong supporter of the Second Amendment; I have had a permit to carry a weapon in Virginia for a long time; I believe that it's important; it's important to me personally and to a lot of people in the situation that I'm in to be able to defend myself and my family," he said.
Since the Sept. 11, 2001, attacks, he said, "it's a more dangerous time" for those serving in government.
"I'm not going to comment with great specificity about how I defend myself, but I do feel I have that right," he said. "We are required to defend ourselves."