"I'm happy to say she's holding her own," says Dr. Michael Lemole Jr., chief of neurosurgery at University Medical Center. "Her status is the same as it was yesterday. She's still following simple commands."
Giffords, 40, was shot in the head and remains in critical condition. Lemole adds that while it's good news the Arizona Democrat has "done so well" with an injury where survival and recovery are "abysmal," he also urges patience.
"This is where we constantly say it's week to week, month to month. I know everyone wants new results every day but as long as we don't backslide and as long as she holds her own, that's good. That keeps us hopeful," he said. "We have to play this according to her timeline, not ours."
Holding Out HopeHer family is also trying to remain hopeful, a family friend tells PEOPLE.
U.S. Sen. Kirsten Gillibrand of New York spoke Monday night to Giffords's husband, astronaut Capt. Mark Kelly, 46, who is in Arizona with his wife.
"I talked to Mark last night and offered that [my husband] Jonathan and I would do whatever they needed," Gillibrand says. "I think he's hopeful. He said he told the doctors that she'll be up and walking in two weeks, just watch."
Gillibrand and her husband enjoyed a double date with Giffords and Kelly just days before the shooting at a Washington, D.C. pizza restaurant. With Kelly based in Houston and Giffords dividing her time between Washington and Arizona, the couple cherished the time they have together, Gillibrand says.
The two women bonded when they were young congresswomen together, and Gillibrand shares Capt. Kelly's optimism about her friend's chances.
"You're going to see her unbelievable spirit and strength," says Gillibrand. "[Kelly is] very hopeful and he knows his wife is extremely strong and has great courage and spirit. If anyone can get through this, it would be her."
Authorities have a suspect in her shooting, Jared Lee Loughner, in custody. He stands accused of opening fire outside the Tucson supermarket where Giffords was meeting with constituents. In total, six people were killed and 14 others wounded in the shooting.