Giffords' brain swelling has remained at about the same level as a day ago -- a good sign, doctors said, because such swelling is the most significant risk for head-trauma patients. Doctors removed nearly half of her skull to allow the brain to freely swell and heal itself.

Dr. Peter Rhee, University Medical Center's trauma director, said after the news conference that he is positive that Giffords won't die and likely will avoid a vegetative state. But he said it 's too early to tell how quickly and to what degree Giffords will recover.

She continued to follow simple commands to lift fingers and her thumb, and she moved parts on both sides of her body, Rhee said.

In a related development, President Barack Obama and First Lady Michelle will travel to Tucson on Wednesday along with three top federal officials -- Attorney General Eric Holder, Associate Supreme Court Justice Anthony Kennedy and Homeland Security Secretary Janet Napolitano, according to the report.

They will attend a memorial event at the McKale Center on the University of Arizona campus.

Obama said earlier that his administration was keeping in touch with families of the victims, Arizona Governor Jan Brewer and congressional leaders, and that there is "no doubt" that plans for a memorial will evolve over the next several days.

"It's going to be important, I think, for the country as a whole, as well as the people of Arizona, to feel as if we are speaking directly to our sense of loss, but also speaking to our hopes for the future and how out of this tragedy we can come together as a stronger nation," Obama said.

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