Jan Brewer in 2016?

Arizona Gov. Jan Brewer announces that she will not seek a third term and will retire at the end of her current term during a press conference held on March 12, 2014, in Glendale, Ariz. AP Photo/Matt York

Until Wednesday, Gov. Jan Brewer, R-Ariz., had kept the door open to running for another term. But with the announcement that she won't seek reelection in 2014, Brewer can consider a different political future.

She's one of the most high-profile Republican governors, though she had made national news for mostly notorious reasons: wagging her finger at President Obama when he visited Arizona in 2012, defending a controversial immigration enforcement bill that was partially struck down by the Supreme Court, and, recently, facing a firestorm over whether she would veto a bill that would have allowed Arizona businesses to refuse service to gays (she ultimately vetoed the measure).

Though her national profile may not draw a lot of crossover appeal from Democrats and independents, there's a wide open Republican presidential primary coming in 2016, and governors (incumbent and former) have often used their posts as a possible springboard to higher office. A recent forum on conservative commentator Sean Hannity's website spent six pages debating the question: Could Jan Brewer run for president?

Not so fast, say several Republican strategists. A Brewer bid is not only unlikely, but inadvisable, too.

"If she jumps in the race for president, she would be adding to the current pool of polarizing and unelectable candidates who are a distraction to the viable," said Trey Hardin, a strategist who has worked on the campaigns of several Republican candidates.

Rick Wilson, a Florida-based GOP consultant, said a run for president is "out of the range of possibility," and John Feehery, another Republican strategist said he "can't imagine she could do much after her tenure as governor."

But Chuck Coughlin, a longtime adviser to Brewer, said the governor's record as a pragmatic problem-solver in Arizona runs far deeper than the handful of topics that have made national news. He pointed to her success in passing five Republican budgets in a row, securing voter approval for a sales tax hike in 2010 that helped cover education funding, and expanded Medicaid under the Affordable Care Act over conservative opposition.

He doesn't think a presidential bid is in the cards - though "I'm sure she'd be flattered to be considered," he said - but that she would prefer to work on public health issues, a longtime passion, resolving the immigration debate, or helping Phoenix win a bid to host the 2016 Republican convention.

Rather than interest in the job, a bigger problem could be electability. Although Brewer could fire up the conservative base, she would "not be a big draw for the Hispanic vote," said strategist Ron Bonjean.

"Nationally she came across as a very controversial figure. It's among Republican primary voters she is popular. But among independents, among much of the rest of the country, she has turned them off," he said.

Bonjean suggested another possibility could be a primary challenge to Sen. John McCain, R-Ariz., for his seat when he is up for reelection in 2016. McCain is in hot water with the state Republican Party, which censured him in January for an overly "liberal" record, and polling shows that his negative ratings have been on the rise. In a February Rocky Mountain Poll, 56 percent of voters rated his performance as "fair" or "poor," including 38 percent of registered Republicans - up from only 27 percent last summer.

Though he has not decided on whether to seek a sixth term yet, McCain said the censure made him think "more seriously" about it.

Brewer had a 32 percent favorable and 30 percent unfavorable rating in February, virtually unchanged since July 2013. Her favorable ratings from Republicans have risen recently, and rising unfavorable ratings from young voters have been offset with support among older Arizonans.

Still, Coughlin said he was confident that a Senate bid "wouldn't be in the cards" because of Brewer's longtime friendship with McCain.

"Despite the disagreements, she's been a lifelong supporter of his and he has been very good with her," he said, noting that McCain would often introduce her when she was campaigning in the 2010 gubernatorial race.

She wants to see the GOP regain the White House, he said, and would be happy to support the people who share that ambition.

She could be a valuable ally for whoever runs.

In 2012, Brewer was one of five Republican governors who met with billionaire casino magnate Sheldon Adelson while in Las Vegas for the Republican Governors' Association meeting in December 2012. A few weeks later, her political action committee reported receiving $250,000 from Adelson and his wife in October. Much of Brewer's cash -- $680,000, according to the Arizona Capitol Times - went to support Arizona congressional candidates including Jeff Flake, who ran a successful race for U.S. Senate.

  • Rebecca Kaplan

    Rebecca Kaplan is a political reporter for CBSNews.com.

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