In a year that sees incumbents across the country dropping like flies, an unlikely one is in a very comfortable position: Arizona Gov. Jan Brewer.

Only six months ago, Brewer presided over a state with a dire budget deficit. She had two dozen challengers in the Republican primary and her approval rating was well below 50%. Then a tough new immigration law landed on her desk. Brewer signed SB 1070 and became the biggest defender of Arizona’s get-tough stance on illegal immigration.

Now she leads her November opponent, Democratic Atty. Gen. Terry Goddard, by a 3-2 margin in polls. Even after a painful debate performance — which featured a 16-second pause when Brewer forgot her opening statement — her numbers improved.

“She came back from the dead because the Legislature handed her 1070 to sign,” said Jim Haynes, president of the Behavior Research Center, which regularly polls in Arizona on political issues. Immigration, he said, has become “one of those issues that comes along and steamrolls everything else.”

Analysts have warned that the Arizona Republican Party, which has embraced a widespread crackdown on illegal immigrants, risks alienating Latino voters and suffering the fate of the GOP in California, which became marginalized after the passage of the hard-line immigration initiative Proposition 187 in 1994.

But any significant growth in Latino votes is far off. For now, SB 1070, coupled with a national mood that favors Republicans, has put the party in a strong position in Arizona, veteran observers say.

“SB 1070 created an environment that gave all of the Republican statewide candidates this year a 10-15% uptick,” said Bruce Merrill, a pollster and emeritus professor at Arizona State University.

The wide-ranging law requires police to determine the immigration status of people they arrest for other reasons if they think those arrested are in the country illegally.

Advocates argued that the law was needed to protect the state, the favorite point of entry for illegal crossings from Mexico, from violence seeping across the border. Critics of the law noted that crime was down significantly on the border and statewide and argued that the law would lead to racial profiling.

In an interview, Brewer said signing the bill was the right thing to do. But she said that other steps she has taken have won her Arizonans’ affections as well — namely advocating a temporary 1% sales tax hike to stave off the collapse of state government, even against the wishes of most of her party.

“I still believe the people of Arizona are concerned about jobs and the economy, and getting our budget under control — and then illegal immigration,” Brewer said. “I have [taken] stands that I thought were right.”

Before this year, Brewer was not known for her stance on illegal immigration. A longtime legislator and Maricopa County supervisor, Brewer was known as a fiscal conservative and 28-year veteran of politics. In January 2009, she was Arizona’s secretary of state, managing 38 employees. When Democratic Gov. Janet Napolitano resigned to become the federal secretary of Homeland Security, Brewer automatically became governor.

Even though she has become a staple on national news shows — local reporters complain that she speaks to Fox News more than Arizona journalists — Brewer still lives in the house in suburban Glendale where she raised her children, and she has been spotted at Walmart and Ross Dress for Less.

She speaks with the sometimes oddball diction of someone who has spent her adult life in the bureaucratic world of state politics. At a news conference this month to warn people about devices that steal credit card numbers at gas pumps, Brewer said: “It is most important that people remain vigilant.... They do not want to be the recipient of being victimized.”

When she became governor, Brewer walked into a budget deficit that was nearly one-third the size of the state’s general fund — on a per-capita basis, one that rivaled California’s as the biggest in the nation. She slashed spending, sold the building that houses her office and made the state the first to withdraw from a federal program to provide healthcare to children just above the poverty line.

But she still struggled to balance the budget. In a tax-averse state, she decided she needed to ask voters to approve the three-year, 1% sales tax hike. Her Republican colleagues in the statehouse were aghast. At one point in the acrimonious budget process, Brewer sued them.

Then, on April 23, she signed SB 1070 — and her poll numbers shot up.

At the time, Brewer had been even with several challengers in the GOP primary who were angered by her proposed tax hike. But in May the tax passed easily with 65% of the vote.

Republicans steadily began dropping out of the primary. One, a wealthy businessman named Buz Mills who spent $3 million on the race, said he couldn’t match the free publicity that SB 1070 gave Brewer. The governor easily won the August primary, even after a federal judge ruled that much of the law is unconstitutional and put it on hold.

Merrill said that Brewer’s embrace of the law has positioned her as a champion for her state. As such, he said, she has garnered sympathy from people who see her 16-second " brain freeze,” as she called her silence in the debate, as only human.

Goddard, Brewer’s opponent, opposed 1070 and said in an interview that Brewer has benefited from simple demagoguery. During the debate, Goddard pushed the governor to renounce her false claim that immigration violence had become so bad that headless bodies were being uncovered in the desert. She eventually did — but only after fleeing reporters as they tried to question her after the debate. On Friday, Goddard released ads hammering at the issue.

“I still can’t imagine the sort of sinister calculation that would lead someone, as chief executive of her state, to do something with malice aforethought that would do so much damage to her state,” Goddard said. “I’ve done more on border security than Jan Brewer’s ever thought about.”

Brewer said she’s surprised at the attention she’s received since signing the immigration law, but says her fans appreciate her because she is true to herself.

“I have been in public service for 28 years,” she said. “People know Jan Brewer and they support her, and I would like to believe that they love her.”

nicholas.riccardi@latimes.com