AP sources: Gunman in Arizona lawmaker's shooting identified as Jared Laughner.
Five people confirmed dead.
Giffords was first elected to represent Arizona's 8th District in 2006. The "Congress on Your Corner" events, which she holds regularly, allow constituents to present their concerns directly to her.
Giffords' Tucson office was one of three damaged last March by vandals who targeted Democrats in advance of the U.S. House vote on the controversial health care legislation. A glass panel at her office was shattered, and at the time her staff said that it appeared the window had been damaged by a pellet gun.
House Speaker John Boehner condemned the attack.
"An attack on one who serves is an attack on all who serve," he said in a statement. "Acts and threats of violence against public officials have no place in our society."
Her fellow Arizona congressman, Republican Jeff Flake, who was reached Saturday on his way to the hospital, recalled that he had last spoken with Giffords on the House floor during this week's swearing-in ceremony.
"We have a fairly small delegation and we've met often," he said of Giffords, who in November beat back a tough challenge from a Tea Party-endorsed opponent.
"She got re-elected because she's tenacious," Flake said. "There was a very strong headwind against all Democrats and people did not expect her to come back to Congress.
"But she was tireless," he said. "Others may have held back after things happen — like the damage to her office. She was fearless."
Flake said emotions have been running high in Arizona over issues, including immigration.
"That's obviously an issue that is a very passionate one for a lot of people," he said.
In a statement released by his office, House Speaker John Boehner said he was "horrified by the senseless attack on Congresswoman Gabrielle Giffords and members of her staff ... this is a sad day for our country."