In a statement released by the gun control advocacy group she started with her husband, Giffords said that "no one piece of legislation" would have prevented the shooting.
"However, I hope that commonsense policies like universal background checks become part of our history, just like the Tucson shootings are — our communities will be safer because of it."
While such checks may keep those with mental illnesses from obtaining guns, the 24-year-old Loughner had never been diagnosed with any conditions, meaning it's doubtful much would have stopped him from legally purchasing a weapon.
Friends and family interviewed by law enforcement after the shooting painted a picture of a young man who was deeply troubled in the weeks before the shooting.
Loughner visited Anthony George Kuck, who had known him since preschool. Kuck said he was alarmed to find he had shaved his head and was armed.
"I kicked him out of my house because he showed me his gun," Kuck said.
Kuck told police he had seen Loughner's mental state deteriorate over time, starting with drinking problems in high school, trouble with authorities and being kicked out of college.
"I know he has some crazy thoughts where he ... just believes the government is corrupt, and he has all these assumptions on things, that he doesn't really know what he's talking about," Kuck told investigators.
While he never heard him mention Giffords "he just seemed to have some kind of ... hate for government," Kuck added.
Kuck's roommate, Derek Andrew Heintz, who has known Loughner since he was about 12, said he was cooking when Loughner showed up with a gun and removed it from his belt. It was loaded with 32 rounds.
He asked Loughner why he had the weapon.