For the GOP — a house divided that faces significant demographic hurdles to winning the White House in 2016 even as it celebrates President Obama’s shellacking — this was huge. A party threatened with electoral extinction among African Americans and immigrants now has someone to brag about in Washington. In a wave election less about fresh Republican ideas than fervid disapproval of all things presidential, Love’s compelling personal story is an oasis. She’s not just a black face in what’s often described as a party full of angry old white men. She’s a path forward.

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It’s hard to overstate how unlikely Love’s victory looked on paper. Utah is less than 1 percent black. Though more than 60 percent of the state’s people identify as members of the Church of Jesus Christ of Latter-day Saints, the church is just 3 percent black. Love, 38, is one of these few black Mormons — part of a church that, until 1978, didn’t let African Americans participate in all church activities and still hasn’t apologized for its racism.

Yet, a woman born in Brooklyn to Haitian immigrants is now a duly-elected representative of the Beehive State. What led to this?

A speech at a national political convention about triumphing over adversity — just like another familiar politician facing long odds.

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At the Democratic National Convention in 2004, Obama spun a tale of unrealistic dreams achieved by the power of a “larger American story.”

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“I owe a debt to all of those who came before me, and that in no other country on Earth is my story even possible,” the future president said. “Our pride is based on a very simple premise, summed up in a declaration made over two hundred years ago: ‘We hold these truths to be self-evident, that all men are created equal.'”

Eight years later, Love turned her superficially similar biography — child of foreigner makes good — into a parable for gritty, individual wherewithal. This was Horatio Alger by the Brooklyn-Queens Expressway.

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Her parents fled Haiti in 1976, one step ahead of the dreaded Tonton Macoutes, the secret police of dictator Francois “Papa Doc” Duvalier. “My parents immigrated to the U.S. with ten dollars in their pocket, believing that the America they had heard about really did exist,” Love told the Republican National Convention, gathered in Tampa in 2012 to nominate Mitt Romney. “When times got tough they didn’t look to Washington, they looked within.”

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Indeed, Love — a black woman who married a white man she met on a Mormon mission, left her Catholic Church and lit out to a white enclave by the Great Salt Lake — explicitly challenged what she described as a vision of America mired in demography.

“President Obama’s version of America is a divided one — pitting us against each other based on our income level, gender, and social status,” she said. “His policies have failed!”

Her father, as she reminds interviewers regularly, worked at several jobs — janitor and factory worker — to get her through college at the University of Hartford in Connecticut. “I remember taking my dad to college with me on the first day of orientation,” she told Fox News in a 2012 interview, “and he looked at me very seriously, and he said, ‘Mia, your mother and I have done everything we could to get you here. We’ve worked hard. We’ve never taken a handout. You’re not going to be a burden to society. You will give back.'”

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A talented performing artist, she reportedly turned down a Broadway role in “Smokey Joe’s Cafe” because it conflicted with her wedding in 1998 to Jason Love, who, by the way, took her to a firing range on their first date. She became a neighborhood activist in Saratoga Springs, Utah, leading the charge to get a developer to spray the area for flies — “The War of the Midges” it was called — ultimately winning a seat on the city council and then being elected mayor of the small town.

Even when she entered what would turn out to be a losing congressional run in 2012, the GOP knew what it had. Even the future Republican nominee for vice president said so.

“Mia has a great opportunity to extend the message of liberty and economic freedom in ways that a lot of us can’t, and we’re excited about that,” said Rep. Paul Ryan (Wis.) after hosting a fundraiser for Love.

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Two years later, Ryan’s enthusiasm was borne out on Twitter after Love’s victory. She trailed Democrat Doug Owens most of the night as the results came in from Utah’s 4th District, but ultimately triumphed with 50 percent of the vote to Owens’s 47 percent. “Many people said Utah would never elect a black, Republican, LDS woman to Congress. And guess what … we were the first to do it,” she told cheering supporters, the Salt Lake Tribune reported.

Damon Cann, a political science professor at Utah State University, told the paper: “Since the election of Barack Obama, the Republicans have been more serious about trying to showcase the diversity within the Republican Party. And Mia Love is potentially the poster child for diversity in the party.”

Just as Obama’s policies didn’t matter as much as the fact that he existed in 2008, Love’s may not either. Judging by her Web site, she won’t upend conservative orthodoxy. She wants to repeal Obamacare. She wants to defend the Second Amendment. She’s pro-life. All-in-all, a typical Republican.

Except: Not at all. Though she may speak out against immigration or D.C. dysfunction, she is not a white-haired, pale-skinned Methuselah turning beet-red on Fox News while doing so. She is a black woman under 40.

That’s all that matters.