Awaiting confirmation:
MSNBC reports that deputy city manager tells them that doctors expect Giffords to "pull through".
And the shooter has been identified:
AP sources: Gunman in Arizona lawmaker's shooting identified as Jared Laughner
Update: From the hospital press conference: Doctor confirms that of the ten patients at the hospital, there is one dead, five in critical condition, five currently undergoing surgery.
Giffords is out of surgery, in critical condition but the doctor is "very optimistic" about her recovery. She was shot once in the head.
The confirmed death is a 10-year old child.