Giffords, a popular 40-year-old Democrat, remained in critical condition at a Tucson hospital but is “holding her own,” responding to simple commands and breathing without aid of a tube although a bullet passed through her brain, doctors said.

“She has no right to look this good. We’re hopeful,” Dr. Michael Lemole, head of neurosurgery at the University Medical Center in Tucson, said of her recovery. “It’s week to week, month to month.”

The suspect in the shooting, 22-year-old Jared Lee Loughner, is being held on five federal charges, including the attempted assassination of Giffords.

The bloody rampage — at an event Giffords hosted for constituents — has fueled debate about whether heated rhetoric seen in recent US political campaigns can lead to violence.

President Barack Obama plans to go to Arizona on Wednesday to attend a memorial service for the dead, who included a federal judge, a 9-year-old girl and one of Giffords’ young aides.

A CBS News poll released on Tuesday found a majority of Americans reject the view that heated political rhetoric was a factor in the weekend shootings in Arizona.

The poll found 57 percent of respondents said the harsh political tone had nothing to do with the shooting, compared to 32 percent who felt it did. Rejection of a link was strongest among Republicans, 69 percent of whom felt harsh rhetoric was not related to the attack.

While the motive for the Saturday attack was not apparent, politicians and commentators have said a climate in which strong language and ideological polarization is common may have contributed.

Lawmakers in both political parties have spoken out on the need for greater civility in politics, and on Wednesday members of Congress will come togteher in a bipartisan prayer service.

Giffords’s colleagues in Congress have put most of their work on hold after the shootings, which prompted many of them to reassess their own security and even their way of life.

The Republican-led House of Representatives has postponed a vote to repeal Obama’s controversial ovehaul of the US healthcare system, which Giffords and other Democrats backed.

In Washington, US Attorney General Eric Holder said the shooting rampage showed the danger posed by threats against public officials.

“Without question, threats against public officials — whatever form they take — continue to be cause for concern and vigilance,” Holder said. “But I do not believe that these threats are as strong as the forces working for tolerance and peace.”

Loughner’s parents, Amy and Randy, are devastated by the incident and plan to release a statement, a neighbor told local media on Tuesday.

“Their son is not Amy and Randy, and people need to understand that. They’re devastated. Wouldn’t you be if it was your child?” neighbor Wayne Smith, with tears in his eyes, told Phoenix’s News Channel Three.

“They’re hurting bad, she’s really bad ... it’s a sad thing, and he told me to tell you guys that when he gets to where he can, he will make a statement himself,” he added.