Updated at 7:41 p.m. ET
The sole suspect in this month's mass shooting in Tucson, Ariz., that killed six people and left 13 wounded, including a sitting congresswoman, pleaded not guilty to the federal charges against him Monday in a Phoenix courthouse.
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Jared Loughner, 22, walked into his second courtroom appearance in the shooting case smiling and wearing an orange prison suit and glasses. Loughner's attorney, Judy Clarke, spoke to him, and he nodded. Security was tight at the hearing. At least eight U.S. Marshals were present.
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Loughner's parents were not in attendance at the hearing, CBS News reports.
Meanwhile, the husband of Rep. Gabrielle Giffords, one of the victims of the Tucson rampage, told the Houston Chronicle Monday that his wife could be out of a Houston intensive care unit by the end of this week, CBS News Correspondent Don Teague reports.
Loughner is charged with the attempted assassination of Giffords and the attempted murder of two of her aides. He is accused of opening fire on a Giffords political event in a rampage that wounded 13 people and killed six others, including a federal judge and a 9-year-old girl who was born on Sept. 11, 2001.
The Tucson man will later face state charges dealing with the other victims.
U.S. District Judge Larry Burns of San Diego asked Clarke whether there was any question about her client's abilities to understand the case against him.
"We are not raising any issues at this time," Clarke said.
Investigators have said Loughner was mentally disturbed and acting increasingly erratic in the weeks leading up to the shooting. If he later pleads not guilty by reason insanity and is successful, he could avoid the death penalty and be sent to a mental health facility instead of prison.
Prosecutor Wallace Kleindienst estimated that he would know within the next 30 days whether additional federal charges would be filed against Loughner. Kleindienst said prosecutors provided defense lawyers with records taken from Loughner's computer and documents of about 250 interviews made in the case.
The judge did not rule on prosecutors' request to move the federal case back to Tucson so that victims and witnesses do not have to make the four-hour round trip drive to Phoenix to attend court hearings. The case was moved because one of those killed was a federal judge.
Clarke said she didn't oppose the request, but questioned where Loughner would be jailed in Tucson if the case were moved.
Both federal and state authorities intend to prosecute Loughner in the Jan. 8 shootings. There will also likely be proceedings over whether to move the case to a different venue, a possible insanity defense, and prosecutors' push for the death penalty, all meaning the case could take years to wend its way through the criminal justice system.
Loughner's next court date is scheduled for March 9.
Meanwhile, the Houston hospital treating Giffords said Sunday that her condition is improving daily, but gave no update on the buildup of brain fluid that .
The hospital treating Giffords gave no update Monday, and spokesman James Campbell said the next update would come when they are ready to move Giffords to the rehab hospital.
A hospital statement said Giffords would continue to receive therapy "until her physicians determine she is ready for transfer" to a nearby center where she would begin a full rehabilitation program.
Giffords was flown to Memorial Hermann Texas Medical Center Hospital on Friday from Tucson. Shortly after her arrival, doctors said she had been given a tube to drain a buildup of brain fluid, which can cause pressure and swelling.
CBS News correspondent Don Teague reports that doctors had hoped to move Giffords into the rehabilitation unit by this stage. The congresswoman is still unable to speak and is experiencing weakness or paralysis on her right side.
"It's improving," said Dr. Gerard Francisco, the chief medical officer at Hermann hospital. "We're continuing to assess that."
In the latest legal move, the U.S. attorney for Arizona in a court filing Sunday asked that the federal case be transferred back to Tucson for all further hearings.
Local federal court rules also require that a crime that happens in the court's Tucson region should be tried there unless a court moves the case.
The case was moved to Phoenix because one of the six dead, U.S. District Judge John Roll, was based in Tucson and federal judges there recused themselves. All the federal judges in the rest of the state soon joined them, and a San Diego-based judge is now assigned to the case.
One area that will help the pace of the case is the fact that it's a relatively simple investigation. Authorities have said Loughner acted alone, and dozens of people witnessed the shooting and surveillance cameras captured it on tape.
Investigators say they have also seized writings from Loughner in which he used words like "I planned ahead," "My assassination" and "Giffords."
Defense lawyers could ask that the case be moved out of Arizona by arguing that extensive negative publicity would make it impossible for Loughner to get a fair trial.
There was so much speculation that San Diego would ultimately be the home for the trial that federal authorities were prompted to issue a statement last week denying the reports and saying it's way too early in the case to discuss.
Clarke has not responded to requests seeking comment. She is one of the top lawyers in the country for defendants facing prominent death penalty cases, having represented clients such "Unabomber" Ted Kaczynski and Olympic bomber Eric Rudolph. She has a reputation for working out plea deals that spare defendants the death penalty, as was the case for Rudolph and Kaczynski.
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