The Twitter account of Fox 11 News Arizona said that a family friend told the station that Giffords "woke up from anesthesia & spoke to people in her room & recognized her husband Mark Kelly."
Politico reported that a source close to the family told them the same thing.
Former Surgeon General Dr. Richard Carmona described the wound Giffords suffered as "devastating," but would not elaborate, the Fox 11 News reported on its website. Doctors at UMC were cautiously optimistic.
Dr. Peter Rhee said he was "very optimistic" about her recovery chances, the station reported. "I'm about as optimistic as you can get in this situation," he said.
Late Update: the Los Angeles Times reports:
Giffords was out of surgery Saturday night and was responsive to some commands from doctors, said Mark Kimble, who works in Giffords' communication office in Tucson.
"The next three days are going to be very critical as far as swelling of the brain. And that's about all we know right now. They're very optimistic though," Kimble said.