Striding on stage to the triumphant strains of Nessun Dorma, Donald Trump has a surprisingly humble confession to make for someone defying all the laws of political gravity.

“Unless we win, it doesn’t mean a damn thing,” the would-be Republican presidential nominee warns a campaign rally in South Carolina, despite finishing his fourth month in a row at the top of the opinion polls. “I want to pick my date for the election. I want it next Tuesday,” he confides to the 11,000-strong crowd – typical of the grassroots support that needs to flourish well into March for him to win the nomination, let alone November’s general election.

Such moments of self-doubt are fleeting, quickly replaced by the now familiar bombast of a billionaire whose status as a “winner” has become his defining policy platform. “Nobody has crowds like we have crowds. It’s a movement. It’s beyond anything,” he continues, back on message.

Trump is not the only one beginning to wonder whether his improbable campaign can confound the pundits and go the distance, particularly after a burst of recent controversy only seemed to cement his polling lead over bewildered rivals. Conventional wisdom holds that any one of these outbursts would have sunk most politicians by now.

First, there was the time he outraged prisoners of war by doubting the heroism of Vietnam veteran John McCain because he allowed himself to be captured. Then there was the first television debate, where he appeared to accuse Fox News moderator Megyn Kelly of asking him tough questions because she was menstruating.

As if PoWs, Fox News and women were not enemies enough, Trump has also accused Mexican immigrants to the US of being rapists, claimed that a Black Lives Matter protester who was violently ejected from a rally deserved to be “roughed up”, appeared to mock a New York Times journalist for his disability, falsely accused Muslim Americans of cheering on the 9/11 attackers, and agreed with suggestions that all such Muslims should have heir names tracked on a database.

And just as critics began to argue that such comments amounted to brutal, racist demagoguery verging on fascism, Trump’s Twitter account recirculated racially charged but falsified crime statistics from an actual Nazi sympathiser.

Trump has complained that many of these incidents were exaggerated by the political media, 70% of whom, he says, are “scum”. But he has nonetheless refused to retract any of the comments. “I could have said, ‘Oh, I misspoke’, but I am not big on that,” Trump tells the crowd in South Carolina. “You have to be wrong.”

Some rivals still hope that, eventually, even Trump’s supporters will tire of what critics view as his relentless attacks on minorities in particular. One poll this weekend shows his support among Republicans down by 12 points – although at 31% he still leads the field.

Other opponents question whether there is much overarching political ideology to Trump at all, simply opportunism and a relish for making waves. “He is an egomaniac, he’s a narcissist. He’s not a conservative, he’s not a liberal, he believes in himself,” former presidential rival Bobby Jindal told the Guardian, shortly before dropping out of the race. “He took Reagan’s slogan about making America great again, [but] he’s about making Donald Trump great.”

Liz Mair, a Republican strategist organising an anti-Trump fundraising committee, worries that many of the comments seen as gaffes by the liberal media are, in fact, carefully designed to boost his standing with his core constituency. “I personally think it’s best that people who don’t like Trump and his policies – whether it’s libertarians like me, establishment Republicans or real, rock-ribbed conservatives – effectively take out an insurance policy and do some work to try to actively undercut him,” she says. “And not just pray for him to commit real political suicide.”

Another well-connected New Hampshire Republican marvels at the political controversies that Trump has weathered. “Just one of these flip-flops, gaffes or lies would have killed a capable, competent campaign,” he says. But, he adds, “if your campaign is based on ‘jumping the shark’, there’s no ‘jumping the shark’ moment”.

Yet there is more to Trump than attention-grabbing outrage. As he delights in telling supporters, the three issues that he rails against most – immigration reform, free-trade deals and Barack Obama’s national security policy – have become perhaps the defining issues of the election.

“Who’s going to be best? Trump, Trump, Trump,” he brags, to an answering chant from supporters that does nothing to dispel the fascistic overtones of Tuesday’s rally in Myrtle Beach, South Carolina.

His policies for deporting every undocumented immigrant in the US and demanding that Mexico pays for a border wall – “A real wall. A very tall wall, taller than that ceiling” – might sound unrealistic, but they have arguably destroyed the campaign hopes of Jeb Bush, who favours immigration reform.

So what might it take to stop Trump? One source of optimism among opponents is the strong evidence that polls this far away from election day can be an average of eight percentage points out, simply because most people have not made up their minds. Among Americans who identify as Republicans, current polls suggest he has 25-30% of the vote.

A survey from Pew Research conducted at the end of September provided more detail about who those individuals are: they are likely to be less educated and less affluent compared to the support base of other candidates. That means Trump’s support base could be problematic on election day. In 2008, Americans who didn’t graduate from college were significantly less likely to register to vote compared with those who did graduate.

In the battle for hearts and minds, converting Trump’s passionate supporters will be hard. To blunt his lead, another candidate would need to tap into his support base without jeopardising their own. Polling experts believe this to be unlikely, as it is hard to imagine anyone doing Trump better than Trump, let alone anyone doing Trump without sacrificing their own support.

A far more likely outcome is that Trump’s base remains solid but his relative lead slowly declines as voters coalesce around either Marco Rubio or Ted Cruz, leaving the real estate mogul from New York looking as forgotten as winners in these early states in past elections, from Pat Robertson in 1988 to Mike Huckabee in 2008.

Trump says what voters are thinking and, the more outrageous he is, the more they agree with him Frank Luntz, pollster

This scenario can be best understood by looking at responses to the question: “Are there any of these candidates you would definitely not support for the Republican nomination for president?” While 20-30% of voters say they would support Trump, another 20-30% say they definitely would not. Other candidates, like Cruz, aren’t quite so divisive (only 5-10% wouldn’t vote for him).

Steve Deace, a prominent Iowa conservative, is one of many who thinks Trump’s ultimate appeal will prove limited. “Trump’s got a locked-in base, no matter what he does,” he says. A vocal Ted Cruz supporter, Deace compares Trump to former Texas congressman Ron Paul in that both candidates had “a high floor and a low ceiling”.

Trump’s antics are “both a good and a bad thing”, he argues. “On one hand, it produces a loyal following that is attracted to that persona which will not leave you. On the other hand, it limits your ability to grow beyond that.”

For now, though, Trump seems to be defying the laws of political gravity and consistently maintaining a lead over a deeply fragmented Republican field. Winning the Republican nomination, therefore, is far from out of the question. Betting markets put this at 7-1 currently. With odds like those, a year out from the election, anyone who calls a Trump victory “impossible” should be eyed with caution. Top Republican pollster Frank Luntz suggests that, at this point, the only thing that could hurt Trump would be if he were “shown to have hurt people who have worked for him … but his comments, as radical as they may be, won’t have much of an impact since the people supporting him agree with him”.

Luntz believes Trump speaks for voters who, for the first time, feel as if they have a mouthpiece and like the fact that they feel like they are being heard. As the pollster notes: “Trump says what they’re thinking and, the more outrageous he is, the more they agree with him. He’s saying what no politician would say, and that’s another reason they like him.”

That is certainly the feeling among ordinary supporters who have attended his increasingly packed campaign events in recent months.

“I like the way he speaks,” says Sandra Murray of Dubuque, Iowa. “He speaks what people need to hear. He may be a little bold, but you can’t sugarcoat things any more. This country is a huge mess and we need to get out of this and, honestly, he could be the man to do it.”

Other supporters offer a simpler explanation. “I wish I had big nuts like him,” concludes Dino Rossi of Newton, Massachusetts. “He’s not afraid of anybody or anything. That’s pretty cool.”