TUCSON — Representative Gabrielle Giffords is still in the hospital, but some of her most ardent backers are so enamored of the idea of her running for the Senate that they describe the inevitable campaign commercials: the deep-voiced narrator recounting what happened to her, the images of her wounded, then recovering and speaking into the camera alongside her astronaut husband to call on Arizonans to unite.

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A tribute to the victims of the January shooting in which 6 people were killed and Ms. Giffords and 12 others were injured.

These supporters say they do not want to get...