"The goal isn't bipartisanship, it's results," Udall said. "But bipartisanship is the only way to get results. ... In the end, we're not enemies, we are fellow Americans."
Giffords herself is still recovering from her injuries. Her right side remains weak and Kelly was at her side Sunday to assist her as she walked on stage at the memorial event. She has made few public appearances since the incident with some rare exceptions such as casting a vote raising the federal debt ceiling and an interview with ABC's Diane Sawyer.
She has been undergoing intensive rehabilitation in Houston, but has returned to Tucson four times since the shooting, according to her office.
Carusone, the congresswoman's chief of staff, said that Giffords has steadily increased her workload as her condition has improved.
"As the year wore on, we were able to plug the congresswoman in more," she said. "Now we talk regularly over video chats and telephone. She's gotten more and more involved the better she gets."
Giffords still has not definitively settled on whether she will seek re-election this year, with Carusone predicting that decision will come in the coming months.
"I think, for her, it's a personal decision (and) whether she thinks she can do the job up to the standards she holds for herself," Carusone said.
As to Loughner, he potentially faces the death penalty if convicted on charges of murdering six people -- including the chief federal judge of Arizona, John Roll. He has been diagnosed as schizophrenic and has spent time on suicide watch while in custody and is undergoing treatment in Springfield, Missouri.
A federal appeals court in May cleared the way for him to be forcibly medicated over the objections of Loughner and his attorney.