Kelly returned June 1 from his 16-day shuttle mission, and is now home to be with his wife.
The couple met in 2003 during a young leaders' forum in China, then married in 2007 in Tucson. Giffords divided her time between Washington, D.C., and Arizona, while Kelly remained in Houston.
The two saw each other whenever and wherever they could.
A judge has declared shooting suspect Jared Loughner mentally incapable of participating in his defense and sent him to a federal facility where doctors will try to treat his condition and make it possible to put him on trial.
With an open Senate seat in Arizona, some Democrats had viewed Giffords as one of their best hopes for winning it, before the Jan. 8 shooting threw her political future into question.
The shooting has created something of a vacuum, with few candidates willing to declare their interest until Giffords' situation is clarified. Carusone has only said that the congresswoman has until May 2012 to decide.
Barber said he hopes she'll return to Tucson soon.
"This is just one of the next really major steps toward her recovery," he said. "I'm sure she'll count this as another step just as we all do."
Associated Press writer Amanda Lee Myers in Phoenix contributed to this report.