Ms. Giffords’s hair, short and wispy for some time after her brain surgery, has returned to its natural bounce. Once heavily guarded by Capitol Police officers and a stream of medical professionals, Ms. Giffords now lives with Mr. Kelly and his 15-year-old daughter, Claire, and Nelson, her service dog, in a modern adobe-style house they bought in August, decorated with bright, large-scale paintings and sculptures.

Ms. Giffords’s ability to understand others is unscathed. During a two-hour interview here, she talked about whether she missed Washington (“a little”); explained, in short phrases, her positions on firearms; and made a sly one-word joke (“wasteland”) about one of her least favorite places. She revealed the provenance of some of her paintings (her old Congressional office), pointed out one that was PG-13 (a semiabstract nude), and lamented what a recent frost had taken from her garden. Once limited to two words — “what” and “chicken” — each month she gains more.

Speaking in full sentences is still a struggle, and she has regular therapy sessions to help recover her speech and to manage her other impairments. Her vision is impaired, and her right leg and arm are largely paralyzed. She can move her shoulder, her hip and slightly her foot.

The rest of her time is largely spent preparing for the legislative battles, political campaigns and potential face-offs with friends and former colleagues that will be waged through her month-old organizations. She and Mr. Kelly are already looking at governor contests, Congressional special elections and 2014 races. They hope to influence the outcome by leveraging the power of their names and their story, an effort presaged last month when Ms. Giffords lit up a Senate Judiciary Committee hearing with her brief and powerful plea: “We must do something.”

“Sometimes there will be some difficult conversations,” Mr. Kelly said. “There already have been.”

For nearly two decades, the National Rifle Association has succeeded in rewarding lawmakers who backed legislation supporting gun rights and firearm manufacturers and punishing those who did not. Those efforts largely overwhelmed the voices on the opposing side.