This morning a massive effort is underway to dissect every aspect of Loughner's life. Investigators are looking at all threats and rants against Giffords in recent days to see if any of those people might have been in contact with Loughner, sources told ABC News. Investigators are also searching for any ties to radical and anti-semitic groups. One name that's come up is a group that's called the American Renaissance, a white supremacist group.
Giffords, 40, was shot in the back of her head, the bullet crossing the left side of her brain and exiting just above her left eye.
Today, Giffords remains in critical condition and her brain swelling has not worsened.
"I assessed Congresswoman Giffords in the last few hours and I'm happy to say she's holding her own. That's to say she is still following those simple commands for us," Dr. Michael Lemole, a surgeon at the University Medical Center in Tucson said.
Lemole said that Giffords is responding to simple commands like squeezing someone's hand or raising a finger.
"It implies that those higher centers of the brain are working. Not only are those areas working, but communicating with one another," Lemole said.
Lemole said that Giffords still faces a tough battle to recovery. Doctors worry about infection and they want to remove her breathing tube as soon as they can to reduce the rise of pneumonia, Lemole said.
"We're not out of the woods. Every day that we get farther out, we are more and more encouraged," Lemole said.
When Giffords' husband, astronaut Mark Kelly, asked her to raise two fingers, she reportedly made the peace sign.
Giffords' family remains at her bedside, the congresswoman's spokesperson said.
Giffords' husband issued a statement late last night.
"On behalf of Gabby and our entire family, I want to extend our heartfelt gratitude to the people of Arizona and this great nation for their unbelievable outpouring of support... Serving Southern Arizonans is her passion, and nothing makes her more proud than representing them in Congress," Kelly said.
"Many stories of heroism are emerging, and they are a source of strength for us during this difficult time. We are forever grateful," Kelly said.
Three heroes have been lauded for tackling the gunman, including Patricia Maisch and Bill Badger.
"Something had to be done...when you see an individual shoots a 9-year-old girl, we have to take him down and we did," said Badger, a retired Army colonel.
Maisch is credited with removing the second magazine from the gunman's left hand when he was attempting to load the gun.
Frantic 911 calls released Sunday show the horror and chaos from Saturday's shooting that left even operators losing their composure.
"Oh my god," exclaims a 911 operator who got the first report of the carnage.
Sally Badger called seeking information about her husband, not knowing he was courageously tackling the gunman and holding him in a chokehold.
"My husband just called me and told me he was shot. He was going to the Gabrielle Gifford event and I don't know where he is," Badger told 911. "He called me and then the phone went dead."
A man who identified himself as Manuel Hernandez told the operator, "There was a shooting at Safeway…Where Gabrielle Giffords was…and I do believe Gabrielle Giffords was hit."
"She's hit. And I do believe she's breathing," he said. "She is breathing. She still has a pulse."