Family: Giffords to Enter Houston Rehab Center

Updated at 8:17 p.m. ET

U.S. Rep. Gabrielle Giffords will be moved Friday to a rehabilitation hospital in Houston to begin the next phase of her recovery from a gunshot wound, barring medical issues that would delay the transfer, her family said Wednesday.

Dr. Peter Rhee told Barbara Grijalva from CBS News affiliate KOLD that Giffords stood on her feet, aided by caregivers Wednesday. She did not try to walk. He also said she sat in a chair today in front of a window so she could see the mountains.

Giffords' husband said his wife's care will continue at TIRR Memorial Hermann Rehabilitation Hospital in Houston, where he lives and works as an astronaut. Doctors say the exact day of the move will depend on Giffords' health.

"I am extremely hopeful at the signs of recovery that my wife has made since the shooting," Mark Kelly said in a statement released by Giffords' congressional office. "The team of doctors and nurses at UMC has stabilized her to the point of being ready to move to the rehabilitation phase."

Complete Coverage: Tragedy in Tucson

Kelly is scheduled to command NASA's last space shuttle flight in April, but that's uncertain now. He has been a constant presence at Giffords' bedside since rushing to Tucson after first getting word of the attack.

Giffords was gravely wounded by a gunshot to the forehead on Jan. 8 as she was meeting with constituents outside a grocery store in Tucson. The gunman shot 18 other people, killing six and wounding 12 more.

Since then, Giffords has been at University Medical Center in Tucson, where her condition has improved almost daily, doctors have said.

Word of the move was met with elation from Giffords' friends and others who have been visiting the three-term Democrat at the hospital.

"It's good news for all of us and for all the people who have been praying for wisdom and strength for the surgeons and others who have been helping her," said Stephanie Aaron, Giffords' rabbi at Congregation Chaverim in Tucson. "It's nothing short of a miracle, but it's also Gabby's will to fight. It's her strength of spirit."

Giffords' neurosurgeon said the family considered hospitals around the country, including in Washington, D.C., New York and Chicago.

"The congresswoman's family wants to ensure she receives the best rehabilitative care possible for her type of serious penetrating brain injury," said Dr. Michael Lemole.

TIRR Memorial Hermann is a 116-bed rehab facility affiliated with the University of Texas Health Science Center in Houston. It claims to have the largest research program on recovery from traumatic brain injury in the world, and gets federal funding for long-term research on such patients.

One of its success stories is Buffalo Bills' tight end Kevin Everett, treated after a life-threatening spinal cord injury in 2007. Everett was paralyzed from the neck down when he arrived at the rehab center in September 2007; now he can walk.

Dr. Jonathan Fellus, director of the brain injury program at the Kessler Institute for Rehabilitation in West Orange, N.J., said it's not surprising that Giffords could enter rehabilitation as early as two weeks after the injury.

"It's not unusual as long as she's been medically and neurologically stabilized," he said. "The sooner the better."

Gloria Giffords said that her daughter had "scrolled through photographs on her husband's iPhone, tried to undo his tie and shirt and even began to look at get-well cards and pages of large-print text taken from a Harry Potter book," the New York Times reported and that "Everyday Gabby improves and shows higher levels of comprehension and complex actions."

But doctors and aides say that the greatest challenges still lie ahead for the congresswoman and that her husband's declaration that she'd be on her feet in two weeks was mostly in jest.

Meanwhile, Kelly said in several broadcast interviews that he believed for about 20 minutes that his wife was dead after viewing a mistaken television news report that said his wife had been fatally shot.

Kelly said he rushed aboard a friend's plane to fly to Arizona, and while aboard the plane saw the TV report.

"I just, you know, walked into the bathroom, and you know, broke down," he said. "To hear that she died is just, it's devastating for me."

Kelly said he learned that she was alive when he called Giffords' mother, who was outside the operating room at the Tucson hospital where the congresswoman was being treated.

Kelly also told Sawyer that he's sure Giffords recognizes him at her hospital bed, since she has continued with a habit of playing with his wedding ring - moving it up and down his finger and sometimes putting it on her thumb.

"She's done that before," he said. "She'll do that if we're sitting in a restaurant. She'll do the same exact movements."

Kelly added that Giffords isn't aware that six people died in the shooting, including Gabe Zimmerman, one of her staff members. He also said he probably wouldn't want her to return to Congress.

"But I know that's probably not going to matter to her. I think she's such a devoted public servant that she's going to come out of this and be more resolved to fix things," he said.