The Democratic congresswoman has been undergoing extensive therapy in the nearly two months since she was shot at a political event in Tucson, and has been receiving frequent visits from her astronaut husband Mark Kelly as he trains to be the commander of the next shuttle mission.
Giffords spokesman C.J. Karamargin said Thursday that the congresswoman also gets regular, detailed updates about the work being done at her offices in Tucson and in Washington. She gets the updates from her chief of staff, Pia Carusone, who is splitting her time between Houston, Washington and Tucson.
Among Giffords' other visitors has been Stephanie Aaron, her rabbi and good friend. Aaron described Giffords' progress to The Associated Press on Thursday after a visit to the hospital over the weekend.
She said Giffords sang Don McLean's "American Pie" with husband Mark Kelly and his two daughters, and that she knew the words better than the three of them. Musical therapy is an important part of her recovery as doctors use song in attempt to improve her brain function, along with physical, occupational and speech rehabilitation.
Aaron said Giffords also chanted a Hebrew healing prayer with her, although the congresswoman didn't know the words beforehand.
Aaron said she would tell Giffords the words, and the two would chant, with Giffords getting frustrated at times.
"I would just stop, hold her hand and say, `Gabby, it's OK. Just breathe.' And we would sit together and just breathe," Aaron said. "And what very much uplifted me was when I was leaving ... she got tears in her eyes and she hugged me. I said, `Gabby, what do you need to remember?' And she said, `Breathe."'
She said when she first arrived at Giffords' hospital room, she brought the congresswoman a giant card made by students at the middle school she attended. Inside it was a T-shirt attached to the card, and printed on the shirt was a photo of the students with Giffords and Kelly when they visited Washington, D.C.
"She reached out and pulled the shirt off and held it to her heart and had a big smile, and she touched the picture of Mark," Aaron said. "It was very moving."
Aaron said that she left the hospital for a while to bring Giffords some of her favorite foods -- matzo ball soup and cheese blintzes. She said Giffords happily ate the meal.
"I'm very encouraged and hopeful for the future," Aaron said.
Kelly will be the commander of Endeavour when it launches in April, and his identical twin brother Scott is the current leader of the International Space Station crew.
President Barack Obama called the astronauts on Thursday to wish them his best. Before signing off, he told Scott Kelly that he spoke to his brother a couple days ago.
"It sounds like Gabby's making incredible progress," the president said, "and we're just thrilled for that."
Giffords was shot on Jan. 8 in a rampage outside a Tucson grocery store that injured 12 others and killed six people, including a federal judge and a 9-year-old girl who was born on Sept. 11, 2001.
Jared Loughner is charged in federal court in the assassination attempt against Giffords that killed six people. Authorities described him as a mentally unstable college dropout who became obsessed with carrying out violence against Giffords for reasons that are unclear.