Giffords was shot point-blank in the head at an event outside a Tucson, Ariz., grocery store Jan. 8. Six people died in the shooting and 13 were injured, including Giffords.
Encouraging news Monday about Giffords' recovery from her gunshot wound: Her doctors say she could get out of the hospital soon.
Her husband tells ABC's Diane Sawyer he sees special signs his wife is getting better.
Monday, Giffords underwent eye surgery to remove bone fragments from her eye socket. Doctors say she continues to do well and could be released to a rehabilitation center in a matter of days.
Just one week after Giffords was gunned down in Tucson, her husband, Mark Kelly, sat down with Diane Sawyer.
In the exclusive interview, Kelly describes how his wife, despite dealing with a near-fatal wound, is trying to communicate -- not by speaking but by smiling and even giving him a back rub.
A NASA astronaut, Kelly met the congresswoman seven years ago at a conference in China.
On their first date Giffords took him on a tour of an Arizona state prison as she was working on capital punishment legislation at the time.
The couple was married in 2007.
When asked if he's open to meeting suspected shooter Jared Loughner's parents Kelly said: "I'd probably see them. You know, I don't think it's their fault. It's not the parents' fault. You know, I'd like to think I'm a person that's somewhat forgiving. They've got to be hurting in this situation as much as anybody."
Kelly alluded to their own family situation, saying: "You know, Gabby and I, Gabby has two stepdaughters. I have children. And they [Loughner's parents] must, I'm sure they love their son. They must be, you know, as distraught over this as all of us are."
It was announced Monday that Loughner's criminal trial will likely be moved to San Diego. Loughner currently being kept in isolation for about 23 hours a day.
Only 10 percent of people survive a bullet to the brain, and some who do, end up in a vegetative state. It is even more rare for people with gunshot wounds to the head to regain all of their abilities, and doctors have cautioned that the full extent of Giffords' recovery remains uncertain.
The Associated Press contributed to this report.