Updated: 6:01 p.m.

Tucson University Medical Center officials said Sunday that they were very pleased with the progress of Rep. Gabrielle Giffords (D-Ariz.) following a gunshot wound to the head and that they were “cautiously optimistic” that she will recover.

Medical Director Peter Rhee said Giffords was able to respond to simple commands following emergency surgery Saturday in which doctors removed a portion of her skull. “Overall, this is as good as it’s going to get” in cases like this, he said.

Giffords, 40, is in a medically induced coma and will have a long road to recovery, UMC chief neurosurgeon Michael Lemole said.

Neurosurgeons “don’t even close the book on [recovery] for several years,” Lemole said, explaining that the lawmaker will likely be in the intensive care unit for at least a week and spend several more weeks in the hospital.

“And no doubt there will be a rehabilitative phase, and that could take weeks or months,” he added.

Because the bullet did not cross the hemispheres of Giffords’ brain, she “is able to communicate,” Lemole said. The doctors stressed, however, that she has not been able to talk.

Giffords was shot at 10 a.m. Mountain time Saturday during an event for constituents in front of a Tucson Safeway grocery store. Police say that 22-year-old Jared Lee Loughner approached the group with a 9 mm Glock semi-automatic handgun and began firing.

Of at least 20 people injured, six died: U.S. District Judge John Roll; Gabe Zimmerman, a 30-year-old Giffords aide who was recently engaged; Christina Taylor Green, a 9-year-old girl who had just been elected to her school’s student council; Dorothy Morris, 76; Dorwin Stoddard, 76; and Phyllis Scheck, 79.

Rhee said that he is “extremely happy with the prognosis” for the others who were wounded, adding, “They are doing relatively well.”

Giffords’ communications director, C.J. Karamargin, told the Arizona Republic late Saturday that Giffords’ district director, Ron Barber, who was wounded in the shooting, was “doing very well” and speaking. There was no update on the condition of Pam Simon, a caseworker for Giffords who was injured.