Gabrielle Giffords: Will she seek re-election?

Rep. Gabrielle Giffords seen here shortly after she made her first trip home to Tucson, Ariz., five months after nearly dying when a gunman shot her in the head during a town hall meeting. / Getty

Sunday marks the one-year anniversary of the tragic shooting in Tucson that claimed six lives and severely wounded Congresswoman Gabrielle Giffords (D-Ariz.).

Giffords and her husband, former astronaut Mark Kelly, will attend a memorial to the shooting victims Sunday at the University of Arizona on Sunday.

Giffords has spent the past year in rehabilitation learning how to walk and talk again. And she must decide whether she will seek re-election.

Kelly told CBS News national correspondent Ben Tracy recently Giffords will decide by May if she'll seek office again.

Kelly said Giffords will decide whether she can do the job. He told Tracy, "You know, it's going to be based on her ability to communicate with her constituents, and whether or not she has the stamina to do that amount of work."

Giffords' recovery has been so remarkable that she now carries on a weekly video conference call with her staff from Houston, where she is in rehab.

Kelly says Giffords struggles to speak, but understands everything. He told CBS News Giffords is constantly updated on what's going on in her district in Arizona and in her Washington, D.C., office.

When asked if there was a moment when the couple considered giving up her seat, Kelly said, "No, no, not yet. She is motivated to get better and return to her job serving the people of Southern Arizona."

Giffords has been back to Tucson three times this year.

She recorded a message for her constituents this fall, saying, "I'm getting stronger; I'm getting better. ... There is a lot to say. I will speak better. I want to get back to work."

Meanwhile her congressional staff has made sure her constituents are still taken care of.

The only vote Giffords made in the past year was to raise the nation's debt limit -- just seven months after she was shot in the head.

But nothing is on hold in her office, except phone calls -- they just keep coming.

Ron Barber, district director in Giffords' office, said the caseload has increased "quite dramatically" since the shooting. "We had a 23 percent increase in constituent requests in the first month, and that's continued," he said.

In Washington, Giffords' staff is working on border security and solar energy issues -- priorities Giffords made just before the shooting.