Nikki Haley speaks during an event. File

But there is buzz, and there is reality. The reality is that Haley, 51, faces a massive uphill battle to take down the former president and gain the Republican presidential nomination – but the sooner the race can be whittled down to her and Trump, 77, the better her still-remote chances.

Trump, according to aggregates of national opinion polls, holds about a 50-percentage-point lead over her, with Florida Governor Ron DeSantis also in the mix. Trump also has large leads in early Republican nominating states such as Iowa and New Hampshire, according to Reuters.

Still, Haley has been gaining ground in some polls on the back of strong performances in debates. The polls show her tied with DeSantis in Iowa and surpassing him in New Hampshire.

“There is a narrow path” to victory for Haley, said Republican pollster Whit Ayres.

That path involves top-tier finishes in both Iowa and New Hampshire and perhaps a victory in her home state of South Carolina, where she served as governor.

That would provide Haley with the things she would need most to have a chance against Trump: momentum, media coverage and money flowing in from anti-Trump donors.

From there, it would be a matter of trying to compete in the larger states later in the calendar such as California and Texas, which award large swaths of delegates.

Opinion polls suggest winning South Carolina, her home state, will be a tall order: according to RealClearPolitics, which aggregates poll numbers, Trump has a 30-point edge over the field there with Haley in second place.

Trump’s edge in Iowa is also about 30 points, where Haley is running third behind DeSantis, and a 27-point edge over Haley in New Hampshire.

Trump has gained strength since facing a battery of legal charges surrounding his attempts to overturn Democrat Joe Biden’s 2020 election win, with voters who were initially reluctant to support him rallying to his side.

To have a chance, Haley needs the field to shrink so that ultimately, it becomes a two-person race between her and Trump, which would allow her to try to knit together the anti-Trump factions within the party, while also perhaps stealing some of Trump’s voters.

In a memo by Haley’s team released earlier in November, campaign manager Betsy Ankney pointed to polling that showed Haley strengthening in Iowa and New Hampshire and Desantis weakening.

So far, Trump’s campaign has trained most of their fire on DeSantis. Should Haley’s rise continue, she would likely face a full onslaught of attacks from the Trump campaign, pro-Trump social media influencers, and related super PAC spending groups.

A Trump spokesperson did not respond to questions about whether the campaign would soon turn its attention to Haley.

Political analysts largely agree that Haley’s best chance against Trump would be facing him head on, without other rivals, but even that would require a significant and perhaps unprecedented swing in Republican voter opinion.

Trump’s free-wheeling, anti-immigration platform remains immensely popular with much of the Republican voter base. Haley, by contrast, is more of a traditional Republican establishment candidate who has campaigned as a foreign policy hawk and fiscal conservative.

While Haley favours a more interventionist foreign policy than the more isolationist Trump and has taken a more hardline stance on abortions than the former president, it is not clear whether she is drawing more support for her policies or for the fact that she is simply not Trump.

Haley, who served as UN ambassador under Trump, further cemented herself as the establishment candidate on Tuesday when the influential Koch network endorsed her and pledged to use its vast resources to promote her candidacy.