She had been breathing on her own since she was shot in the head, but doctors had left the breathing tube in as a precaution.
Authorities said suspected gunman, Jared Lee Loughner, targeted Giffords last Saturday when he went on a shooting rampage that left six people dead and 13 people, including the congresswoman, injured.
Meantime, the Safeway grocery store in Tucson, Ariz. where the shooting happened reopened on Saturday.
"Our employees have been through so much but they are here, they're working and kind of anxious to reconnect with their customers and the community. We're doing OK," store spokeswoman Cathy Kloos said.
New video of the suspect has been released. Loughner made the video in September, shortly after he was expelled from his biology class for a disruptive outburst.
The video prompted Loughner's suspension from Pima Community College, just hours after it was viewed by campus police.
"This is Pima Community College, one of the biggest scams in America. The students are so illiterate that it affects their daily lives," Loughner is heard saying in the video.
The Associated Press contributed to this report.