Timothy Stanley is a historian and columnist for Britain's Daily Telegraph. He is the author of "Citizen Hollywood: How the Collaboration Between L.A. and D.C. Revolutionized American Politics." The opinions expressed in this commentary are solely those of the author.

(CNN) Donald Trump defies his critics, which is one of the things his fans love about him. Loud, crude, philosophically ill-defined -- he ought to have crashed and burned as a Republican presidential candidate weeks ago.

Yet his big win in the New Hampshire primary finally proves that his national poll ratings can be turned into votes. Trump can win. Trump must be stopped.

Trump is a real estate magnate who helped transform the New York skyline in the 1980s, before moving into casinos and a retail empire that includes a tacky clothes-line. He previously identified as both an independent and a Democrat, before apparently shifting to the Right a decade ago.

When he entered the Republican presidential primaries , many of us wrote it off as a publicity stunt. The fact that it was such bad publicity should have told us we were wrong. Trump went after illegal immigrants -- branding many of them as "rapists" , while asserting that "some, I assume, are good people" -- and promised to surround the country with a wall.

From that the pundits deduced that he was far-right, if not a nationalist, like Marine Le Pen of France . But his appeal proved more complex.

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On some domestic issues he is more left-wing: health care, infrastructure spending and tax. On social issues, like immigration, his tough guy appearance strikes a chord with people who feel they've been betrayed by weak national leadership and silenced by political correctness.

They revel in the shamelessness of a man whose fortune means he's beholden to no one -- and who doesn't look like he cares whether he wins or lose.

Americans choose their presidential candidates in a series of state-wide elections or primaries -- and Trump lost the first Republican contest in Iowa . That was probably because the state is heavily religious and winners there tend to have a good ground game. But he won in the more secular New Hampshire with an interesting constituency that includes self-described moderates and new voters.

In other words, the Trump campaign poses a challenge to the Republican Party leadership and its conservative establishment. The leadership has failed to fight back because it is hopelessly divided.

Can moderate Republicans unite to defeat Trump?

In New Hampshire there were four establishment-type moderates running: Jeb Bush , Chris Christie, Marco Rubio and John Kasich . Each has strengths and weaknesses. Kasich, governor of Ohio, came second and has a good claim to lead the fightback against Trump. But he lacks the money and organization necessary to mount a long campaign through these complex, expensive primaries. Jeb Bush has the most dollars and activists, but has underwhelmed the voters.

There is a chance to stop Trump in South Carolina on February 20. That state is more ideologically conservative, with a stronger local party leadership and a tradition of preferring mainstream candidates. But if the moderate field remains divided, it's quite possible that Trump will win again.

And that would be bad for all of us. Trump has served some useful purpose: he has punctured the arrogance of the establishment and proven that character can beat big money in U.S. politics. But he represents the politics of protest, and that rarely translates into good government.

His characterization of Mexican migrants -- legal or otherwise -- is wrong and damaging at a time when America is evolving towards a less-white society. His stance on Muslim immigration , which he would cease until the terror threat is brought under control, is racist.

Trump does not care about the things that regular conservatives have dedicated their lives to fighting for: controls on abortion, protection of marriage, reform of the healthcare market. His inclination towards expanding the government and putting it on the side of his people isn't terribly constitutional. And his claim in a debate that the purpose of conservatism is to conserve wealth is spiritually impoverished.

The Republican Party needs to stop him -- and sooner rather than later.