Giffords' Mom: Gabby Could Enter Rehab Friday

Updated 2:09 p.m. ET

Rep. Gabrielle Giffords is recovering with surprising speed and could be moved from the hospital to a rehabilitation center Friday, her mother Gloria said in an e-mail to friends and family Tuesday, according to a New York Times report.

Doctors and aides to the congresswoman, who was shot at an event with constituents Jan. 8, warned that her mother's e-mail might overstate the gains Giffords has made and that no decision has been made on moving her from the hospital.

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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 Times reported and that "Everyday Gabby improves and shows higher levels of comprehension and complex actions."

Giffords may have also smiled and moved her limbs on command, according to Gloria Giffords.

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.

A spokesman for Giffords said Wednesday her family is considering rehabilitation centers in Houston and New York as the congresswoman recovers.

Mark Kimble, who works in Giffords' Tucson office, told The Associated Press the family has not made a decision yet. Her doctors have said she could move to a rehab center within days.

Houston is where her astronaut husband, Mark Kelly, is based. Kelly is scheduled to command NASA's last space shuttle flight, but that's uncertain now.

But Dr. Michael Lemole, the neurosurgeon treating Giffords told CBS News correspondent Stephan Kaufman that he cannot comment on any possible move and that ""those news outlets that are confirming this are not in a position to confirm that."

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.

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