They really got to know each other at the next year’s meeting of the group, in Arizona, when Mr. Kelly, who had divorced, and Ms. Giffords passed up an aerial tour of the Grand Canyon. They hiked instead, “talking about our lives and how really hard it can be to be single,” Ms. Giffords said. “I had dated some big players, but they weren’t really nice men, and I was a little gun-shy. Mark talked about his love for his two daughters, about sharing custody.” As they spoke, Ms. Giffords wondered if this conversation was the start of something more.

They began a long-distance phone and e-mail friendship during which she would sometimes coach him on dating other women. (“Call her the next day to say thanks, even if you didn’t have a great time,” she once said.)

Then Ms. Giffords, who had broken up with her boyfriend, contacted Mr. Kelly in November 2004 and suggested an unusual get-together. “I invited him to join me on a tour of the Arizona State Prison in Florence,” she said. “I’d been working on legislation dealing with capital punishment. Mark is the son of police officers — well, he just really wanted to sit in ‘the chair.’ ” And he really wanted to know her better. “She had it all,” he said. “Beautiful, smart, hard working, balanced, fun to be with, and she laughed at my jokes.”

When she began her Congressional campaign in 2005, he began showing up at her campaign stops. Ms. Giffords showed up for the launching of his shuttle mission on Discovery in 2006, and chose a wake-up song: “Beautiful Day by U2.”

Image The bride, an avid recycler, borrowed the gown. Credit... Norma Jean Gargasz for The New York Times

“When our relationship just kept getting deeper, I felt a huge sense of relief,” she said. “I had found someone like me. We’re both really curious. We’re focused on the same things.”