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Jared Lee Loughner has reportedly invoked his fifth amendment right against self-incrimination.

Gabrielle Giffords, a 40-year-old Democrat elected to Arizona's 8th District in 2006, was holding a "Congress on Your Corner" event at a Safeway in northwest Tucson when witnesses say a man started firing indiscriminately, striking her in the head at point blank range.

She remains in critical condition at University Medical Center in Tucson.

Former U.S. Surgeon General Richard Carmona has worked with Giffords for several
years. He got emotional as he talked to reporters about her chances of survival and
recovery.

"There are lots of complications that occur with problems like this, so you know, she's in our thoughts, in our prayers. We're all hoping for the best for her," Carmona said. "But I've taken care of a lot of people like this before, I know how difficult a path it is to recovery. I saw the CT scan, the MRI, I saw what was done, I know the surgery that was done. With guarded optimism, I hope that she will survive. But this is a very devastating wound."

U.S. Marshal for Arizona David Gonzales confirmed to the Associated Press that U.S. District Judge John Roll died in the attack.

A nine-year-old girl was also killed. She was the granddaughter of former Philadelphia Phillies manager Dallas Green.

In a statement released by the White House Press Secretary, President Obama called the shooting a "senseless and terrible act of violence [that] has no place in a free society."

Watch the video to see a press conference held by local authorities at the University of Arizona Medical Center.

The Associated Press contributed to this report.