But if anyone can change that, many believe it's Giffords's husband Mark Kelly.
The question is whether he wants it.
Kelly had his biggest turn on the political stage Wednesday at a Senate Judiciary Committee hearing on gun violence, and the reviews were strong.
But while Kelly and Giffords have made clear that they will be players in politics -- through both a political action committee (Gabby PAC) and a super PAC described by some as the anti-NRA (Americans for Responsible Solutions) -- it's not clear that Kelly is interested in realizing his wife's political goals. Namely, running for statewide office.
Kelly has the kind of profile that political recruiters drool over. He's a retired astronaut, a strong public speaker, and he has banked a significant amount of goodwill over the last two years. What's more, the fundraising involved in the couple's new ventures is great experience for a political campaign.
But even those close to Giffords and Kelly have no idea what the future holds for Kelly.
"I have no idea if he'd be interested," said Republican former Kentucky secretary of state Trey Grayson, who is a co-chair of Gabby PAC. "Obviously, he has a lot of attributes that would make him a strong candidate if he wanted to run -- good personal narrative, charisma, smart, drive, been in outer space, Gabby's network of volunteers and donors."
Compounding the desire for Kelly to run is the fact that the Democratic bench remains thin in the Grand Canyon State. Former U.S. surgeon general Richard Carmona (D) acquitted himself well during his 2012 Senate run and over-performed President Obama at the top of the ticket, but beyond that, it's not clear who might step up in the future.
One aide close to the Giffords/Kelly orbit said the speculation at this point "seems to be based more on hopes rather than facts."
"The hopes are heightened due to the reality ... that the bench is not so deep after Carmona," the aide said. "Having said that, if (Kelly) runs, he’d obviously have an instant political operation at the ready, with top-level strategists, name ID, media savvy, military chops and big fundraising capacity. He'd be a major force."
Beyond Kelly and Carmona, Democrats point to Phoenix Mayor Greg Stanton, Rep. Ann Kirkpatrick (who recently returned to Congress after losing her seat in 2010) and freshman Rep. Kyrsten Sinema. Kirkpatrick and Sinema, notably, have both won competitive districts.
But few would engender the kind of excitement in Democratic circles that Kelly would.
"Mark and Gabby are focused on Americans for Responsible Solutions," said another Arizona Democrat close to the family. "But that doesn't mean that they won't look at other opportunities in the future."
Those future options include the 2014 governor's race, in which Gov. Jan Brewer (R) may or may not be term-limited. And Sen. John McCain (R-Ariz.) will be up for reelection in 2016, when he'll be 80 years old and could retire.
Kelly was thought by some to be a potential candidate for Giffords's old House seat and the state's open Senate seat in 2012, but he passed on running for either. Former Giffords' aide Ron Barber (D) won her House seat, while Republican then-Rep. Jeff Flake defeated Carmona in a competitive Senate race.
Before the tragedy in Tucson, Giffords built an impressive electoral record in the House, holding a Republican-leaning district in a very tough year in 2010, as other Democrats in similar districts -- even longtime incumbents -- lost in the GOP wave.
Any Democrat who would run statewide would need to run strong in Tucson-based Pima County, and Kelly would undoubtedly have a leg up in that region. Beyond that, it's about keeping it close in the rest of the state -- particularly Republican-leaning Maricopa County.
Kelly and his wife are also gun owners (he said Wednesday that he and his wife are "pro-gun ownership" but "anti-gun violence") and his wife ran as a supporter of gun rights in her previous campaigns. Kelly also reached out to NRA head Wayne LaPierre after Wednesday's hearing -- after firmly disagreeing with LaPierre's stance against increased background checks -- which suggests he's hoping to remain someone that advocates on both sides of the gun issue feel comfortable with.
That may be aimed at the super PAC's political goals more than Kelly's own, but it certainly wouldn't hurt if Kelly were to attempt a run in a red state.