PHOENIX » Republicans in the state Legislature here push a law that would require President Barack Obama to provide his long-form birth certificate in order to get on the Arizona presidential ballot in 2012. The governor uses Facebook to denounce the president’s "backdoor amnesty plan." Cars traveling on State Route 260 are treated to a giant billboard bearing Obama’s mug on a mock $100 trillion bill that asks, "But Who Will Pay the Piper?"

Given the openly hostile environment, Obama would seem to have little chance of winning Arizona’s 11 electoral votes in 2012 or even the incentive to make much of an effort here. But the state’s crackdown on illegal immigration has coincided with a boom in its Hispanic population, now nearly a third of the state’s residents.

That has created what Obama strategists and some residents see as a surprising opportunity to compete in a Republican state that was off the map for Obama in 2008, when it was the home of his opponent, Sen. John McCain. The sense has been reinforced by the hard-line stance most of the Republican presidential field has taken on immigration and the party reaction against Newt Gingrich’s recent call for a "humane" policy.

The Obama campaign, which is counting on Hispanic voters to help carry friendlier territory like Colorado and Nevada, has opened offices in Phoenix, Tucson and Flagstaff in a play for Arizona, and it has helped recruit a Hispanic candidate for Senate. Activists are mobilizing to generate turnout by emphasizing the president’s efforts on behalf of Hispanics, in contrast to the anti-immigration efforts of state Republicans.

"I tell them about the Dream Act," said Miriam Gonzalez, 23, who has been registering voters at Latino supermarkets like Ranch Market and Food City, referring to the White House-backed legislation that would provide young Hispanic students a path to citizenship but has been stalled by Republican opposition in Congress. "I keep talking, and then people register."

The voting-age population of Hispanics in Arizona has surged over the past nine years to 845,000 from 455,000 and now constitutes 19 percent of Arizona residents of voting age. Though Hispanics have not turned out at high levels in past years, Democratic activists and Obama campaign officials believe this year could be different, especially after Hispanic voters flexed their expanding muscle in recent local elections, including one this month that recalled a Republican state senator, Russell Pearce, the architect of the state’s tough immigration law.

Thousands of Hispanic residents who had never voted also flooded the polls to help Daniel Valenzuela, a Hispanic firefighter, beat Brenda Sperduti, a white businesswoman, to become the first Hispanic to represent an overwhelmingly Latino district on the Phoenix City Council.

And Greg Stanton, a Democrat, beat Wes Gullett, a Republican, amid record turnout in the race for mayor of Phoenix, in a replay of Tucson, where Jonathan Rothschild soundly beat Rick Grinnell to become the first Democrat to lead that city since 1999.

Valenzuela, the Phoenix councilman-elect, said he spent the past year "knocking on the doors of people whose doors had never been knocked on before," in largely Latino neighborhoods.

"This was a campaign for social behavioral change," he said. "I would ask people, ‘What do you do when you’re frustrated?’ And they would say, ‘I march."’

His reply became almost standard, he said: "If the people who marched actually voted, we wouldn’t have to march in the first place."

Now, Obama campaign strategists say they are taking Arizona seriously.

"I’m completely focused on metrics, and I’m not going to waste money," said Jim Messina, Obama’s campaign manager, referring to the campaign’s decision to open offices in the state, where Obama won 45 percent of the vote in 2008 despite McCain’s advantages. "Arizona is the one state in the country where we didn’t play hard in 2008."

Campaign experts still consider Arizona a long shot for Obama. If the election were held today, "Obama would lose handily," said Bruce Merrill, a professor emeritus at Arizona State University. But, Merrill added, "there are some things going on here that could be more favorable a year from now for Obama."

Among the factors working against the president in Arizona is the housing bust, which has hurt Arizona more than most other places. About half of the homeowners with mortgages in the state owe more than their houses are worth, and the same is true of about 60 percent of commercial properties with mortgages. Arizona is not the only place where Obama is hoping to take advantage of demographic changes. Although Obama’s support among blue-collar white voters has been weakening, and his prospects in traditional presidential bellwethers like Ohio and other industrial states are shaky, the campaign is trying to shore up an alternative Western strategy that expands the electoral map.

Campaign officials say they will still fight hard in the Midwest, but they are plotting an alternative strategy that seeks to take advantage of demographic changes in the West. The Democratic National Committee has been running Spanish-language ads for Obama in Arizona, Colorado, Nevada and Florida.

"It’s about flushing out the Hispanic vote," said Robert Meza, a Latino state senator from Phoenix.

Meza said Latinos in Arizona were worried that the state had moved too far to the right on the political spectrum. "People feel that if it goes any further, they will be even more scapegoated," he said.

Such sentiments are helping to motivate residents like Raquel Contreras, a 19-year-old Mexican-American sophomore at Arizona State University, who was working the phones one recent night to drum up support for Obama’s re-election campaign.

"I personally registered my two brothers to vote — and they’ve never voted before," Contreras said. "I’ll be handcuffing them to myself on Election Day and dragging them to the voting booth."

Obama successfully courted Richard Carmona, a surgeon general in President George W. Bush’s administration who is Puerto Rican, to run as a Democrat for the U.S. Senate seat being vacated by Jon Kyl, a Republican who is retiring. If Carmona, a Tucson resident and self-described independent, wins the Democratic primary, he could be a magnet for Hispanic voters.

Another factor that Democrats say could help drive turnout in the Tucson area is the potential re-election campaign of Rep. Gabrielle Giffords, a popular and sympathetic figure, given her battle to recover from being shot in the head in an assassination attempt.

A Democratic presidential contender last carried Arizona in 1996, when President Bill Clinton beat Bob Dole. But the state has trended rightward as residents have recoiled against a flood of illegal immigration, culminating with the approval of SB 1070, as it is referred to here.

That measure, enacted in 2010, put stringent new requirements on immigrants and gave local law enforcement the power to determine the legal status of those who were stopped and hold those who could not verify that they were legal residents. Its implementation was later blocked, and there was an outcry against it here and nationally.

Three weeks ago, Pearce, who sponsored the law and was one of the state’s most powerful legislators, was ousted from his seat representing an eastern Phoenix suburb, losing a recall election by 8 percentage points, 53 percent to 45 percent, helped by local business leaders suffering from boycotts of the state.

That election and other victories this month have convinced some Hispanics that Obama could pull an upset here and capture a state that, like some others in 2008, had been considered unwinnable.

"Look, he did it in North Carolina and Indiana in 2008," said Trevor Gervais, 18, a freshman at the University of Arizona who has been making phone calls and canvassing for Obama in Hispanic neighborhoods in Tucson. "There are so many places where he never had a chance. Why not Arizona?"

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