Throngs of sign-carrying well-wishers lined the streets in Tucson to wave and cheer.
"She responded very well to that -- smiling and even tearing a little bit," said Dr. Randall Friese, a surgeon at the University Medical Center trauma center in Tucson. "It was very emotional and very special."
Friese and Giffords' doctors in Houston spoke Friday afternoon at a news conference at Texas Medical Center. Doctors say Giffords has a drain in her brain because of a fluid buildup, so she will stay for now in the ICU because of the risk of infection. Parts of her skull were removed after she was shot in the forehead, and they have not yet been replaced, so Giffords is wearing a specially made helmet to protect her brain.
It will be at least next week before she is moved to the center's TIRR Memorial Hermann rehabilitation hospital, and she faces months of rigorous therapy.
Doctors say she'll have her first rehab session in the ICU Friday afternoon.
"She looks spectacular," said Dr. Dong Kim, neurosurgery chief at UTHealth.
A gunman shot Giffords and 18 other people Jan. 8 as she met with constituents outside a grocery store in Tucson. Six people died; all other survivors have been released from the hospital. The suspect in the attack, Jared Loughner, 22, of Tucson, is being held in federal custody.
Giffords has been making progress nearly every day at University Medical Center in Tucson. Her husband, Houston-based astronaut Mark Kelly, tweeted Friday: "GG going to next phase of her recover today. Very grateful to the docs and nurses at UMC, Tucson PD, Sheriffs Dept....Back in Tucson ASAP!"
Kelly traveled with Giffords, along with her mother, a doctor and other medical workers. She napped as a specially outfitted jet took her to Houston, then a helicopter took her from the Houston airport to the ICU at Texas Medical Center, where she'll be evaluated before going to the center's rehabilitation hospital, TIRR Memorial Hermann. U.S. Capitol police arrived Thursday afternoon to set up extra security measures at the 119-bed facility.
Despite the steady progress, doctors warn Giffords has a long road to recovery. Doctors are not sure what, if any, disability she will have.
She moves her lips, but it's not clear whether she is mouthing words, nor how much she is able to see.
"Not everyone always gets 100 percent restoration, but we help them to get to a new normal," said Carl Josehart, chief executive of the rehab hospital that will be Giffords' home for the next month or two.
Dr. Gerard Francisco, the hospital's chief medical officer, will coordinate her care.
"It's going to be a very big team that will address different impairments, but they will have to work together," he said.
First, they'll check her vital signs -- make sure her blood pressure and heart rate are good. Then specialists ranging from physical and occupational therapists to speech therapists and psychologists will give a slew of tests to see what she can and cannot do.
They'll determine the strength of her legs and her ability to stand and walk; the strength of her arms, and whether she can brush her teeth or comb her hair; whether she can safely swallow on her own; how well she thinks and communicates -- not just her ability to speak but also to understand and comprehend.
While she is moving both arms and legs, it's uncertain how much strength she has on her right side; the bullet passed through the left side of her brain, which controls the right side of the body.
Giffords will stay at Memorial Hermann until she no longer needs 24-hour medical care -- the average is one to two months. Then she can get up to five hours a day of physical and other rehab therapies on an outpatient basis, Josehart said.
"It's hard to speculate on the trajectory or course that any one patient will have," he said.
Sometimes, areas of the brain that seem damaged can recover, said Mark Sherer, a neuropsychologist at the rehab center.
"Some of the tissue is temporarily dysfunctional, so the patient appears very impaired very early on after the injury," but may not be permanently damaged, he said.
Kelly said Giffords would be proud of the way Tucson has responded. Memorials continued to grow Friday outside the hospital, in front of her office and at the scene of the shooting.
"I know one of the first things Gabby is going to want to do as soon as she's able to is start writing thank you notes," he said.
Al Garcia came on his Harley Davidson to stand along the ambulance route as Giffords left, as people waved flags and signs.
"We want to be here to help her and show her a good farewell, and hope that she has a great recovery," Garcia said. "It's through all of these prayers that she's leaving in just two weeks."
The Tucson medical team is returning to Arizona on Friday, and nurse Tracy Culbert said they said their goodbyes. Friese, the Tucson surgeon, said it was wonderful to see the support from Tusconians.
"We love her. We're going to miss her while she's here, but this is where she needs to be," he said.