Donald Trump remains the overwhelming favourite for the Republican presidential nomination, but Nikki Haley is surging. If the former president shows any signs of weakness when voting begins next week, her long-shot bid could become a real threat.

On a snowy morning in Iowa this week, in the middle of an Irish pub, Republican presidential candidate Nikki Haley was giving her stump speech: a tight 13 minutes on spending cuts, education reform and a secure southern border.

At the heart of her pitch was this: a Haley presidency would be a return to normalcy, a drama-free alternative to the current frontrunner, former president Donald Trump.

"Don't you want that again? Because we could have that again," she said.

The line won the loudest applause of the morning from the hundred-odd voters who had braved the icy roads to hear her speak in Waukee, on the edge of the state capital Des Moines.

Eleven months into her candidacy, Ms Haley, 51, seems to finally have the wind at her back.

Heading into the Iowa caucuses on Monday, the first contest in the 2024 Republican race, the former South Carolina governor has claimed a series of well-timed victories - consolidating support from deep-pocketed donors, racking up endorsements and steadily advancing in the polls.

"She's engaging, she's smart, she's personable and I think she has a vision of where we should be 10 years from now," said Haley supporter Doug Stout after watching her speak on Tuesday.

The vision was for the "shining city on the hill" type of Republican Party, he said. "The one I grew up with."

The unfortunate reality for the Haley campaign, however, is that not enough voters seem to be buying that vision. Most polls, including in Iowa, suggest Mr Trump maintains a lead of around 30 points.

Observers say Nikki Haley is running a campaign for the wrong era of Republican politics; that her candidacy ignores the reality of the modern Republican party, whose base has turned so definitively toward Mr Trump that the establishment-friendly conservatism favoured by Ms Haley no longer makes sense.

"Ms Haley's campaign represents a misunderstanding of where the base is and what the base wants," said Gunner Ramer, political director for the Republican Accountability Project.

"To those that want the old Republican party back, Haley is offering a very attractive candidacy. But there aren't enough Republicans out there who do."

So what exactly is her game plan?

Ms Haley's allies say both privately and publicly that she is playing to win.

They insist that as the field narrows, and Ms Haley becomes the clear alternative to Mr Trump, she will pull ahead, propelled by moderates and a growing swathe of Republican voters who have tired of the former president, or are concerned about his chances in the general election.

In Iowa, Ms Haley looks poised to swipe the second place spot from Florida Governor Ron DeSantis.

At a Wednesday evening debate between the two, Ms Haley strained to position herself as Mr Trump's sole rival. "I wish Donald Trump was on this stage. He's the one I'm running against," she said.

Ms Haley may be helped by the sudden exit of anti-Trump candidate, Chris Christie, who suspended his campaign this week. Supporters of the former New Jersey Governor, surveys suggest, are most likely to flock to her.

Less helpful was Mr Christie's hot-mic moment, when he was caught saying she would "get smoked", presumably by Mr Trump.

"She's not up to this," he said.

Long-time observers counter that Ms Haley has a knack for defying expectations.

"If you look at her career, a lot of people have underestimated her and a lot of people have been wrong," said Randy Covington, a veteran journalist from South Carolina.

Even her critics acknowledge that she is a master of retail politics - the door-knocking and handshaking that delivered her to the statehouse in 2005. She stunned her own party in the primary by unseating Larry Koon, then the longest-serving member of the House. At the time, Ms Haley had no political experience and was a bookkeeper for her family's clothing shop.

Nearly 20 years later, the state representative-turned-governor-turned-UN-ambassador still likes to introduce herself first as an accountant. She points out that she is a mom of two, the wife of a combat veteran and the child of Indian immigrants, running to make her family proud. In televised debates, in pancake houses and town halls, Ms Haley pauses mid-speech for a smile and pointed eye contact. She's a down-home American hard at work for your vote.

"She connects, she has the X factor," said David Wilkins, a former South Carolina House speaker who led Ms Haley's transition to the governor's house. "The more people who are exposed to her, the more support she's going to get, it's just that simple."

Ms Haley's campaign often looks and sounds like something out of 2012: more compromise and pragmatism, fewer grievances and conspiracy theories. She is a staunch conservative, but she speaks with nuance on hot button issues like abortion and immigration, and is less eager to wade into the country's culture wars.

In Iowa this week, it was clear this was central to her appeal. Voters said they valued Ms Haley's tone and her civility - a clear departure from Mr Trump, who spent part of this week in a federal appeals court for one of the four separate criminal cases he now faces.

"She's boring," one Iowan said of Ms Haley, before quickly clarifying he meant it as a compliment. "We need to get out of the era of politics that is dominated by what someone tweeted."

Polls suggest Ms Haley's measured approach could make her the most formidable opponent to President Joe Biden in November's general election.

"Trump is head-to-head with Biden on a good day," she said this week, before citing a Wall Street Journal poll from late last year. "I defeat Biden by 17 points."

But she has to defeat Mr Trump first.

"This is still the party of Donald Trump, until the Republican party says otherwise," said Jimmy Centers, an Iowa Republican political consultant.

At least one-third of Republican primary voters are thought to be in the "always Trump" camp - a group both devoted to the former president and repelled by the establishment politics embodied by Ms Haley.

"I think she's just more of the same… and Trump isn't," said Mike Williams, an Iowa resident. "I want someone who's a bit of an outsider."

The vice-like grip Mr Trump has on the party doesn't give Ms Haley much room for manoeuvre.

She needs to appeal to two very different groups of Republicans: the "never Trumpers" who despise the former president, as well as those who still like him but worry he will lose to Biden. She has to distance herself from him without alienating his supporters who might yet be persuaded to back someone else.

Ms Haley has been cautious in her criticism of her old boss. At a televised town hall in Iowa, a prospective backer sheepishly admitted he had voted for Mr Trump twice. "Me too," she quipped, beaming.

In nearly every speech, she performs a tightly rehearsed juggling act. Mr Trump "was the "right president at the right time", she'll say. "But rightly or wrongly, chaos follows him".

Those close to Ms Haley shot down the suggestion that she may eventually join his ticket as the vice-presidential nominee - something the Trump campaign has also dismissed. But Ms Haley has said yes to him before, when she became his ambassador at the United Nations.

Mr Trump, for his part, has turned his ire increasingly on Ms Haley, whom he dubbed "birdbrain" in September. "She is a globalist," he said last week. "She likes the globe. I like America first."

The escalating critiques are perhaps the clearest sign that the frontrunner is taking her campaign seriously. Some Trump aides have also been downplaying expectations of a blowout victory in Iowa.

The Republican race will not be decided this month. But the upcoming votes in Iowa and New Hampshire will be the first test of whether Mr Trump's power is as strong as it seems. If not, Ms Haley will be waiting in the wings.