“Until she’s really talking, giving a speech,” Dr. Langer said, “you won’t know if there’s a subtle speech problem. But it sounds like with rehabilitation, with time, she ought to be very functional.”

The use of singing, he said, is a standard technique to help restore speech in people with brain injuries. (It is sometimes used to help treat stuttering, Dr. Langer said, citing the movie “The King’s Speech” in which King George VI sang to overcome his speech impediment.) The part of the brain that controls singing is not the same as the one that controls speech, though it is close.

Dr. Langer also said it was good news that Ms. Giffords was walking. “People’s ultimate endpoints are often based on how rapidly they improve,” he said. “If there’s rapid progress, the recovery potential is much higher. It sounds like she hasn’t plateaued yet and is improving really quickly.”

The specialized clinic that is helping Ms. Giffords recover has several gymnasiums equipped for people with spinal and brain injuries, as well as a swimming pool for therapy. The main hallway is lined with large photographs of former patients who have made spectacular recoveries, among them Kevin Everett, a former National Football League player who suffered a spinal injury.

There are plaques with the inspiring tales of the survivors next to the photos. One shows a man hunting ducks in a wheelchair, his shotgun up and a dog by his side. Another is a bride on her wedding day, who had suffered a traumatic brain injury two years before.

Therapists push patients in wheelchairs along the hallways. Some brain-injury patients who have had parts of their skulls removed, like Ms. Giffords, wear helmets to protect their brains. (In Ms. Giffords’s case, her mother said, doctors are planning to reinstall a section of her cranium at the end of the month, well ahead of schedule.)

Mockups of stairs, a kitchen and a washing machine help patients relearn basic skills. A therapist encouraged one patient to try moving his leg and was caught by an unexpected kick. She winced as she said, “Good, Jim!”