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Mrs. Brewer has been in Arizona politics for decades, having served in the state House and Senate and as a member of the Maricopa County Board of Supervisors. In 2002 she was elected secretary of state, and became governor in January 2009 when Ms. Napolitano, who was the state’s chief executive, became Mr. Obama’s Homeland Security secretary.

In a little more than two years in office, she has signed temporary tax increases to try to close a budget shortfall and has faced key tests on education and gun rights.

But there is little doubt that the immigration issue has dominated her time in office. A year ago, she became the face of anti-Washington sentiment when she signed the toughest state immigration-crackdown legislation in the country, and then went to court to defend it against the Obama administration.

At the time she signed the bill, she was running for re-election and trailed Terry Goddard, who was attorney general, through much of spring 2010. But almost immediately after she signed the bill, polling swung in her direction and she cruised to a 12-percentage-point victory over Mr. Goddard.

In legal challenges to the law, a federal district court and then an appeals court ruled in favor of the Obama administration and halted the key enforcement provisions. Mrs. Brewer is pondering whether to go straight to the Supreme Court or to ask the full 9th U.S. Circuit Court of Appeals to hear the case.

Almost exactly a year after she signed the immigration bill into law, Mrs. Brewer was in spotlight over another set of conservative measures that the state Legislature sent her.

This time, the governor disappointed her conservative backers and won grudging praise from Democrats after she vetoed three of the bills.

One would have allowed guns to be carried on public rights of way at state colleges, another would have required presidential candidates to produce their birth certificates to get on the state’s ballot and a third would have permitted the state to join an interstate compact designed to circumvent Mr. Obama’s health care law.

The bill regarding birth certificates garnered the most attention. Mrs. Brewer said she did not trust putting so much ballot-access control in the hands of one person, the secretary of state, and she doubted the measure would clear a Justice Department review under Attorney General Eric H. Holder Jr., to whom Arizona is required to submit under the Voting Rights Act.

“I know how they work, and I know who’s in charge of the Department of Justice, and I cannot imagine Holder ever approving of that piece of legislation. So bottom line, it wouldn’t have went anywhere anyway,” she said.

Some Arizona pundits argue that Mrs. Brewer is testing her postelection freedom and returning to more moderate Republican roots, with which they say she is more comfortable. They say she is free to do so since she is term-limited and cannot run again in 2014.

But she dismissed talk of a leftward turn.

“Oh, absolutely not. I’ve been a conservative my whole life, but I always do, again, vote and take everything into consideration, and then I do what I believe is the right thing to do,” she said.

The vetoes drew an acknowledgment, but not much more, from Mr. Cherny.

“Anyone with a grain of common sense would have vetoed those bills,” the state Democratic chairman said. “As opposed to some in the Legislature, my issue with her is not that she’s on a fringe conspiracy theorist, but that she puts politics ahead of governing.”