Giffords is unable to open her eyes and cannot speak because of the ventilator, according to Rhee, but she is able to respond when asked to squeeze her hand or hold up her fingers.
"We take those simple commands for granted but they demonstrate high functioning in the brain," said Rhee.
Rep. Giffords was there for a "Congress on Your Corner" event, one of several events she had planned in her Arizona Congressional district to meet with her constituents.
The dead have been identified as the 63-year-old Roll, 30-year-old Gabriel Zimmerman (Giffords' director of community outreach), 76-year-old Dorthy Morris, 76-year-old Dorwin Stoddard, 79-year-old Phyllis Scheck, and 9-year-old Christina Green, according to the Pima County Sheriff's Department.
Loughner legally purchased a Glock 19- 9mm gun at Sportsman's Warehouse in Tucson on Nov. 30, law enforcement officials said. It's unclear if he bought the extended clips used with the gun during the mass shooting. An extended clip holds 30 rounds, officials said.
Pima County Sheriff Clarence Dupnik described the alleged shooter as "mentally unstable."
Dupnik lauded three individuals -- at least one of whom was shot herself -- for tackling Loughner to the ground before he was able to load another magazine into his gun.
Authorities released a photo of the other person of interest -- a white male between 40 and 50 years old with dark hair -- and said he was last seen at the event and may have a connection to Loughner.
The congresswoman was the clear focus of the gunman's assault, Dupnik said.
"He ran through the crowd and when he got to [Giffords] he just started shooting," the sheriff said.
"The anger, the hatred, the bigotry that goes on in this country is getting to be outrageous. And unfortunately Arizona I think is the capital. We are the Mecca for prejudice... for prejudice and bigotry," Dupnik said.
"When I looked up, he was shooting at Congresswoman Giffords," Steven Rayle, an eyewitness, said. "He didn't stop shooting, he just continued shooting rapidly. It was close quarters so people had nowhere to get away from."
"He didn't seem agitated, he seemed determined and just let loose with a barrage of bullets," Rayle said of the gunman.
Rayle told ABC News that "another man went running off" after the shooting, but wasn't sure if the other man was involved. Rayle said the gunman approached Giffords and shot her before turning his gun on other people randomly.
"The whole thing unfolded in about 12 or 15 seconds. As he came around it I laid down on the ground and acted as if I was shot."
After Giffords was shot in the head, staffers rushed to her aid, Rayle said.
"She was conscious, one of her staffers had a coat held to her face," Rayle said.
After ducking under a concrete pillar, pretending to be wounded, Rayle helped tackle the gunman. He grabbed the suspect's feet.
"He didn't really say anything except like, 'you're hurting my arm.' He was defensive, tense and struggling," Rayle said.
Giffords, a representative for Arizona's 8th District who just won reelection to a third term, has been the target of conservative political opponents in recent months.
Last March, Giffords' office was vandalized just after she voted in favor of the health care reform law. The intruders destroyed a glass door and a window at her Tucson Congressional offices.