"We're not out of the woods yet," Lemole said during a news conference at the hospital. "At this phase in the game no change is good, and we have no change."
A major concern for the doctors is to control the swelling in Giffords' brain. They have put the 40-year-old Democrat in an induced coma and removed part of her skull to ease the stress and pressure on the brain.
Lemole said there may be "a collective sigh of relief around the third or fourth day. We're getting close."
He warned, however, that it's not uncommon for swelling to fluctuate in the days after an injury like hers, but said, "Every day that goes by and we don't see an increase we are slightly more optimistic."
Lemole also said that Giffords continues to respond to "basic commands," but declined to specify her movements or what kinds of commands she has been given.
"When I say someone follows simple commands it could be someone showing their thumb, showing two fingers," he said, adding that Giffords is still on a breathing tube and cannot speak.
Giffords is one of eight patients at UMC and one of two in the intensive care unit.
Doctors at UMC say several of the patients have already undergone surgery, including Giffords, and that more surgeries for some of them are still needed.
"We've have vascular injuries, we've had orthopedic injuries, we've had extremity injuries as well," said Dr. Rhee.
All are expected to survive, he said.
While Giffords' team of doctors remain focused on her head injury, they are already preparing for the psychiatric care that she and her fellow shooting victims will need in the weeks and months after the physical recovery has ended.
Depression and post traumatic stress disorder in the patients and their caregivers is common, Rhee said, after a trauma like this.
""We have psychiatrists in house, social workers, some of the best in the country in here," he said.
ABC News' Chief Health and Medical Expert Dr. Richard Besser said the bullet's trajectory is the reason she's still alive, noting that 90 percent of people shot in the head do not survive.
"She has already beat a lot of odds," he said. "Bullets that stay in the head do a lot more damage."