Pima County Sheriff Clarence Dupnik said Giffords was the target of a gunman whom he described as mentally unstable and possibly acting along with an accomplice.
He said Giffords was among 13 people wounded in the melee that killed six people, including Arizona's chief federal judge, a 9-year-old girl and an aide for the Democratic lawmaker.
He said the rampage ended only after two people tackled the gunman.
Doctors were optimistic about Giffords surviving as she was responding to commands from doctors despite having a bullet go through her head.
The anger, the hatred, the bigotry that goes on in this country is getting to be outrageous," the sheriff said.
"And unfortunately, Arizona I think has become the capital. We have become the mecca for prejudice and bigotry."
The reaction to the shooting rippled across the country as Americans were aghast at the sight of such a violent attack on a sitting member of Congress.
The shooting cast a pall over the Capitol as politicians of all stripes denounced the shooting as a horrific and senseless act of violence.
Obama dispatched his FBI director to Arizona. Capitol police asked members of Congress to be more vigilant about security in the wake of the shooting, and some politicians expressed hope that the killing spree serves as a wakeup call at a time when the political climate has become so emotionally charged.
Police say the shooter was in custody, and was identified by people familiar with the investigation as Jared Loughner, 22.
Officials said he used a semiautomatic 9-mm pistol with an extended clip to carry out the attack. U.S. officials who provided his name to the AP spoke on condition of anonymity because they were not authorized to release it publicly.
Giffords, 40, is a three-term moderate Democrat who narrowly won re-election in November against a tea party candidate as conservatives across the country sought to throw her from office over her support of the health care law.
Her office in Tucson was vandalized in the hours after the House passed the overhaul last March as anger over the law spread across the country.