For the past month, Giffords (D, Ariz.) has been undergoing intense physical therapy at a rehabilitation center in Houston, gaining the ability, not only to speak, but to interact with her family and friends.
In an "Early Show" interview, Pia Carusone, Giffords' chief of staff, said the congresswoman isn't fully aware of what happened the day in early January suspected gunman Jared Loughner allegedly opened fire on a crowd gathered for her political event.
Carusone said, "She certainly knows that there's been a traumatic event here. The details of the severity of the injuries to the others, you know, she doesn't know yet about. But she will in time, when she's, you know, at a higher level of communication. Doctors have said it's not really fair, as you can imagine, to tell something so tragic to someone that might not have the ability to ask the detailed questions that someone will have when they hear this news."
CBS News correspondent Don Teague reported that, in the nearly six weeks since Giffords was shot, doctors have called her progress nothing short of remarkable. However, phyisicians caution the long-term damage is still difficult to measure.
Dr. Jonathan Fellus, a neurologist and neuro-rehab specialist, said, "The long-term issues are really going to be focused on language -- her communication abilities, reading, writing, and of course moving that right arm as well."
But friends say these "long-term issues" are obstacles she is determined to overcome.
Rep. Debbie Wasserman Schultz (D, Fla.) said, "You could see she really wanted to engage. And she wanted to be responsive and she really responds with facial expressions and smiles and frowns. But I also saw a little frustrationin wanting to try to respond, because she understood and she wasn't yet able to (respond)."
Teague added, "Giffords has a long recovery ahead of her, but doctors have repeated that her healing has been nothing short of miraculous."
When "Early Show" co-anchor Erica Hill asked about Giffords' abilities to speak, Carusone replied, "There's various words in her vocabulary that are coming back, and new words every day that we hear. Short phrases, simple thoughts. There's no doubt that she understands what's happening around her."
Carusone continued, "She laughs at the appropriate times."
Carusone said Giffords can watch TV. She and husband Mark Kelly, an astronaut, watched "30 Rock" together last week, Carusone said.
"When the conversation turns serious she, I think, can sense that, Carusone said. "So (she) fully recognizes people that come in to visit her. So no one that has seen her has any doubt that she can understand everything around her. And you know, she's just working really hard. And progressing, it's paying off, and every day there's new progress that you see. So, you know, we feel very hopeful at her recovery."
Carusone described Giffords' rehabilitation at TIRR Memorial Hermann Hospital in Houston as "busy."
"They've got a track record for putting together a really great rehab program," Carusone said, "So, it's multi-faceted. I mean, you know, there's different teams of therapists that work on speech and physical and occupational therapy. Obviously, eating is a big part of getting better, and sleeping. I mean that's, you know, basics that we all know. So she does a lot of those things."
Carusone told CBS News Giffords is doing standing, strengthening and flexibility exercises. Her posture, she said, is great, but currently, she cannot walk on her own.