Any discussion of who’s likely to succeed outgoing Sen. Jon Kyl of Arizona needs to factor in the following: If Rep. Gabrielle Giffords wants the seat, it’s hers.

The three-term Democratic congresswoman explored the idea of running for the Senate seat in the event of Mr. Kyl’s retirement before she was shot Jan. 8 at a constituent meet-and-greet in Tucson. Her rehabilitation from a gunshot wound to the head reportedly is proceeding faster than expected.

Mr. Kyl announced Thursday that he would not seek a fourth term in 2012. If Ms. Giffords decides she’s game for a Senate run and if her health permits, she would be virtually impossible to defeat, said Bruce Merrill, Arizona State University professor emeritus and longtime pollster.

“If one assumes she’d be healthy enough to run, there’s nobody who could beat her,” said Mr. Merrill. “Now she’s got 100 percent name identification and 100 percent sympathy from the public. If she was well enough and she wanted the nomination, I don’t think there’s any question.”

That’s the easy scenario. If Ms. Giffords declines to run, then the Senate race becomes much more complicated, with as many as a dozen Republicans, a handful of Democrats, a couple of tea partyers and a member of President Obama’s Cabinet in the mix.

Pencil in Rep. Jeff Flake as an all-but-guaranteed candidate for the Republican nomination. Within minutes of Mr. Kyl’s announcement in Phoenix, Mr. Flake received the endorsement of the influential Club for Growth.

“We definitely hope Congressman Flake takes a look at this and gets into the race,” said Club for Growth spokesman Mike Connelly. “Arizona obviously has a lot of conservative folks who would do a good job, but Congressman Flake has distinguished himself during his tenure in the House as a pro-growth, limited-government conservative.”

The Club for Growth’s support isn’t just for show. Its ads on behalf of Sharron Angle was crucial in helping her defeat her better-known rivals in last year’s double-digit Nevada Republican primary.

The Arizona Republican field could be equally jammed with credible candidates. Potential contenders include Rep. Trent Franks, former Rep. John Shadegg and J.D. Hayworth, Maricopa County Sheriff Joe Arpaio, and state Senate President Russell Pearce.

Democratic hopefuls may have to hold their breath until Ms. Giffords makes her decision. If she doesn’t run, then Homeland Security Secretary Janet Napolitano becomes the immediate favorite, followed in no particular order by businessman Jim Pederson, who ran against Mr. Kyl in 2006, Phoenix Mayor Phil Gordon, former Attorney General Terry Goddard and former Rep. Harry Mitchell.

Ms. Napolitano was elected to two terms as Arizona governor, but her popularity in the state has dipped along with the White House’s fortunes. Yet few doubt she could make a comeback with a combination of name recognition, campaign experience and access to Mr. Obama’s contributors.

Would Ms. Napolitano be interested in returning to the campaign trail? Absolutely. “Her dream has always been to serve in the U.S. Senate. That’s been her lifelong goal,” said Mr. Merrill.

The Democratic Senatorial Campaign Committee released a jubilant statement saying Mr. Kyl’s imminent departure has “instantly catapulted Arizona to a prime pick-up opportunity for Senate Democrats this cycle.”

In the absence of a Giffords candidacy, however, that may be wishful thinking. The current political climate strongly favors Republicans, who knocked off a number of Democrat incumbents in November without losing any of their own.

Can Republicans hold on to the Kyl seat? “I don’t know why they wouldn’t,” said Goldwater Institute communications director Le Templar. “[Sen.] John McCain won handily last year. Every Republican running for statewide office won last year.”

Mr. Kyl, 68, joins an illustrious group of incumbents opting to leave the Senate in 2012. The others are Kent Conrad, North Dakota Democrat; Kay Bailey Hutchison, Texas Republican; Joe Lieberman, Connecticut Independent, and Jim Webb, Virginia Democrat.

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