A nine-year-old girl and a federal judge were among six people killed, and at least 14 others were wounded before bystanders at the event in Tucson on Saturday grappled a gunman armed with a 9mm Glock pistol to the ground.
Alleged shooter Jared Loughner, a 22-year-old local resident, was due to appear in court later Sunday to face federal charges, according to FBI chief Robert Mueller.
Giffords was helped by the fact the bullet did not go through both hemispheres of her brain, traveling instead the length of the left side of her brain, an area that controls speech.
"We're very encouraged by that. We are still in critical condition. Brain swelling at any time can take a turn for the worse," said Michael Lemole, the head neurosurgeon who operated on Giffords.
Trauma chief Peter Rhee cautioned: "We don't know what is going to happen -- what her deficits will be in the future or anything like that.
"This wasn't a grazing wound to the brain. This wound travelled the length of the brain on the left side," he said.
Giffords, from President Barack Obama's Democratic Party, was meeting constituents outside a Tucson supermarket Saturday when the gunman shot her at point blank range before spraying bullets on the small crowd.
The motivation for the shooting remained unclear. Loughner, a failed army recruit, had filled the Internet with angry and largely incoherent condemnations of the government.
A Loughner profile posted on YouTube listed Karl Marx and Friedrich Engels's "The Communist Manifesto" and Adolf Hitler's "Mein Kampf" among his favorite books.
A witness who helped wrestle Loughner to the ground said it seemed the suspect had come ready to kill even more people because he had two more ammunition clips and a knife in his pockets.
"He was ready for war, he was not playing around," Joe Zamudio told CNN. "He was blank. He was callous, almost."
Pima county sheriff Clarence Dupnik said three bystanders tackled the shooter after he stopped shooting to reload his gun. A woman jumped on him at that point and tore an ammunition magazine away from him.
The gunman managed to reload with another magazine -- but a spring apparently failed, and then two male bystanders wrestled him to the ground, restraining him until police arrived.
If the gunman had managed to re-load and resume firing, "there would have been a huge catastrophe," said the sheriff.
Giffords, like most rank-and-file legislators, traveled with no security detail, despite threatening incidents during the recent bitter campaign that saw the Democrat re-elected in a typically Republican-leaning state.
Married to NASA astronaut Mark Kelly, Giffords is the first Jewish woman elected to Congress in Arizona. She barely survived a bruising re-election bid last year to a Republican rival from the right-wing Tea Party movement.
The attacks have shaken official Washington and -- although the motivations of the shooter are unclear -- raised concerns that the toxic political climate could be feeding violence.
"To try to inflame the public on a daily basis... has an impact on people, especially those who are unbalanced personalities to begin with," said sheriff Dupnik on Sunday.
The last major political shooting in the United States was in 1981 when then president Ronald Reagan was shot and injured at a Washington hotel.
The only member of Congress ever to die in the line of duty was Leo Ryan, a California Democrat killed in 1978 in Guyana as he investigated a cult that later carried out a notorious mass suicide.
The House of Representatives has called off proceedings in Washington for the upcoming week and the flags will fly at half mast in honor of the Giffords staffer who died.
Conservative standard-bearer Sarah Palin had controversially placed Giffords on a political hit list, putting her under an image of a gun's cross-hairs for her support of Obama's health care overhaul.
Palin offered condolences for the victims, writing on her Facebook page: "We all pray for the victims and their families, and for peace and justice."
Obama on Sunday called on Americans to observe a "moment of silence" Monday at 1600 GMT to honor the victims of the shooting.
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