Rep. Gabrielle Giffords of Arizona was "holding her own" Monday morning after being shot through the head at an outdoor event to meet constituents two days earlier, but doctors - while optimistic - warn she is still in critical condition and her road to recovery will be long.
Giffords, 40, remained in intensive care at a Tucson hospital. She is still in critical condition and heavily sedated with a breathing tube in place.
Dr. Michael Lemole, the chief of neurosurgery at the University Medical Center told CBS' "The Early Show" co-anchor Erica Hill on Monday that it would be at least another few days to a week before Giffords could hopefully be declared "out of the woods."
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Late Sunday night, Gifford's 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.
Doctors said Sunday she had responded repeatedly to commands to stick out her two fingers, giving them hope she may survive. Lemole told CBS News that those same tests would continue on Monday.
Lemole said Sunday that the trajectory of the bullet that hit Giffords during the attack on the Democratic lawmaker made them optimistic about her recovery.
The brain surgeon said it was good news that she was able to follow simple commands from the doctors and that the bullet did not cross from one hemisphere of the brain to another. Giffords can't speak yet or open her eyes.
"One thing I'm going to emphasize here is we take those kind of simple commands for granted, but they imply a very high level of functioning in the brain," Lemole said.
Lemole gave an account of how surgeons were able to get Giffords into the operating room within 38 minutes of the attack. He said they were quickly able to control the bleeding, which was not severe or excessive.
"She is still in critical condition, brain swelling at any time can take a turn for the worse," Lemole said.
Lemole said that during the surgery, doctors removed bone fragments caused by the bullet fracture to take pressure off the brain. They also removed some devitalized brain tissue, but, Lemole said, "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 craniotomy: "The hair gets shaved. The scalp gets flapped backwards, and a large portion of the cranium skull bone is drilled away. That portion 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."
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Lemole said Monday morning that he remained "cautiously optimistic," and he cautioned that, while he and other members of the hospital staff will be more certain of her survival in a matter of days, the degree to which she will likely be able to recover from her injuries may take much longer to assess.
"We don't close the book on recovery for years, so it will take as long as it takes," Lemole told "The Early Show's," Hill.
Of the nine other wounded victims in the hospital, Dr. Ashton reports that three have been downgraded from critical condition to serious; six are in fair condition.
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.
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In spite of optimism about the congresswoman's responses, Dr. Peter Rhee, the trauma director at the University of Arizona, emphasized on Sunday that Giffords' wound was incredibly serious.
"This wasn't a little grazing wound through the brain; this was a devastating wound that traveled the entire length of the brain on the left side," Rhee said.
"The neurosurgeons, Dr. Wan and Dr. Lemole saved her life," added Rhee.
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.
About 200 people gathered outside Giffords' Tucson office Sunday evening for a candlelight vigil.
Earlier in the day, people crammed the synagogue where Giffords has been a member, as well as the Mountain Avenue Church of Christ, which lost one member in the attack and saw another one wounded.
"I don't know how to grieve. This morning I don't have the magic pill, I don't have the Scripture ... I can't wrap my head around this," said the church's Rev. Mike Nowak, his strong preacher's voice wavering.
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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.
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."