"At this phase in the game, no change is good, and we have no change," Dr. Michael Lemole, chief of neurosurgery at the University of Arizona Medical Center, said Monday afternoon.
Giffords, 40, heavily sedated with a breathing tube in place, but was able to follow simple commands, such as lifting two fingers and giving a thumbs up to doctors. CAT scans shows there is no progression of swelling of the brain.
"We're not out of the woods yet; that swelling can sometimes take three days or five days to maximize. But every day that goes by and we don't see an increase, we're slightly more optimistic."
He said the incidence of swelling from such trauma injuries may peak on the third post op day, which would be Tuesday. "I've seen it go out to as far as ten days," Dr. Lemole said. "Most often the third day. That's why we're much, much more optimistic" about her condition thus far.
He said if there is no swelling by Tuesday, doctors can breathe "a collective sigh of relief."
A 22-year-old manwith wild beliefs steeped in mistrust faces a federal court hearing Monday on charges he tried to assassinate Giffords and killed others in the Tucson shooting rampage on Saturday.
The bullet entered Giffords' brain on the left side, moving from back to front. In most people, the left side of the brain controls their right-sided strength and sensation, as well as the ability to understand and speak - including the ability to understand commands, Lemole said.
Lemole said the fact that Giffords can follow simple commands implies not only that are the centers of her brain are working but that they are communicating with one another.
Giffords is continually assessed by both doctors and nursing staff, even with her sedation on. "We're expecting to see reactions," Dr. Lemole said.
Doctors have not progressed to more complex commands. "That kind of assessment would come, for example, when we remove the breathing tube," Lemole said.
Of the 10 patients treated at the medical center, two remain in the ICU (on in critical condition), and six are in fair or good condition. Two have been discharged.
There are still additional operations to be undertaken by the patients. But Dr. Peter Rhee, trauma director at the University Medical Center, pointed out that while their surgical phase nears an end, the very important issue of trauma care must still be engaged.
"This is a time period when it is very emotional for us. We are accustomed to taking care of post traumatic stress syndrome," Dr. Rhee said.
The patients will survive from a physical standpoint, he said, but added, "We have to bring them back as a whole human being, and that's what we try concentrate on as a trauma center, more than just whether you're alive or dead."
Psychological help is to be directed not only to the victims but to their families and their care providers. "This has had a tremendous impact on all of us," Lemole said.
During surgery, Lemole said, doctors removed bone fragments caused by the bullet fracture to take pressure off the brain. They also removed some devitalized brain tissue, but, he added, "I'm happy to say we didn't have to do a whole lot of that."
CBS News medical correspondent Dr. Jennifer Ashton described the surgery, called a decompressive craniectomy: "The hair gets shaved. The scalp gets flapped backwards, and a large portion of the cranium skull bone is drilled away. (That area of the skull left open, with the brain covered by a synthetic material and then scalp, so that the brain can swell and not have any vital blood supply or tissue compromised) That portion (of skull) remains in a refrigerator for up to, potentially, two-to-three months, and (that area of the brain) is left open so the brain can swell and not impair other parts of the brain."
Rhee said Giffords' condition is not typical of most trauma patients where the skull is intact, since a portion of her skull was removed: "In blunt trauma and other traumas where the skull's intact is where we really get concerned. The pressure is off everybody, no pun intended here."
A moment of silence in honor of the Arizona shooting victims was observed across the country at 11 a.m. ET. President Obama led the moment of silence with White House staff on the South Lawn.
Giffords' brother-in-law, astronaut Scott Kelly, led a moment of silence from the International Space Station.
Kelly spoke of his unique vantage point high above the Earth: "As I look out the window, I see a very beautiful planet that seems very inviting and peaceful. Unfortunately, it is not.
"These days, we are constantly reminded of the unspeakable acts of violence and damage we can inflict upon one another, not just with our actions, but also with our irresponsible words," he said.
"We're better than this. We must do better."
Three of Giffords' staff members were shot, and one died from his wounds. Gabe Zimmerman, 30, served as Giffords' director of community outreach. He was engaged to be married.
"Gabe was a social worker and wanted to help people," Giffords' communications director C.J. Karamargin told Erica Hill. "He was beloved and trusted in our office, he was beloved and trusted in the community."
"It's very hard, it's very difficult," he told "Early Show" anchor Erica Hill.
A Facebook page commemorating Zimmerman has been launched.
Also wounded was Rob Barber, Giffords' district director, and community outreach worker Pam Simon.
Giffords' office had previously been vandalized, on the day of the health care reform bill vote (Giffords supported the measure).
Karamargin admitted he was fearful following the assassination attempt: "Yeah, a little bit," he told Hill. "My office is surrounded by windows, and the venetian blinds for the first time, even at night, they were closed shut."
But he also praised the outpouring of support coming from citizens for the congresswoman and the other victims: "This is a reflection of what type of community Tucson is, but it's also a reflection of Gabrielle Giffords."
Late Sunday night, Giffords' husband, astronaut Mark Kelly, said she had been shot while "doing what she loved most - hearing from her constituents."
"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," said Kelly in the written statement, in which he also expressed his family's condolences for the other victims.