Rep. Giffords (Creative Commons)

Dr. Peter Rhee, the hospital's medical trauma director, said Representative Giffords is one of four victims of Saturday's shooting still hospitalized.

"We're confident she is making progress now," Dr. Michael Lemole, University Medical Center's chief of neurosurgery said. "She is beginning to carry out more complex sequences of events, of activities, in response to our commands."

Lemole also noted that some of Giffords' movements were spontaneous, including when she opened her eyes on her own on Wednesday.

Though Rhee said Thursday that the next step will be to remove Giffords' breathing tube and have her sit in a chair, he pushed that step back to possibly Saturday, according to the Los Angeles Times.

Once the breathing tube is removed, doctors said, Giffords' progress can shift towards rehabilitation, as doctors can finally assess how far she has come and how much work she has left to do.