Giffords was hospitalized after being shot at a public event in Tucson, Arizona.
The congresswoman is in critical condition after undergoing surgery Sunday morning. Doctors are optimistic for her survival, stating they are "very, very encouraged" by her ability to respond to basic commands, according to the San Francisco Chronicle.
Giffords is among the 16 who were injured during the shooting. Six people were killed including US district Judge John Roll, and the 9-year-old granddaughter of former Philadelphia Phillies manager Dallas Green.
Senator Diane Feinstein said Sunday, “My heart sank when I heard the news of the tragedy in Tucson. My thoughts and prayers are with Representative Giffords and her family, the family of Judge Roll and all the other victims and their loved ones. Representative Giffords is a beacon of courage and hope in our nation right now. She bravely pursued her duties as a member of Congress, despite having been the target of vitriolic political rhetoric in the past."
Local sheriffs, in coordination with the FBI are investigating Jared Lee Loughner, who is in custody. Officials believe he may have had an accomplice, who is still unidentified.