There has never been a presidential candidate like Donald Trump.

He inspires and frightens the Republican Party in almost equal measure. While his poll numbers continue to tick upwards, Republican operatives are planning a campaign to try to take him down.

They're attracting big-money investors for a series of attack ads aimed at derailing a campaign many thought would have hit the buffers long before now.

But there's a concern that there is nothing they can do to stop him because the rules don't seem to apply to "The Donald".

He's dominated the headlines in recent days because of his anti-Muslim comments. And it's worth taking a few minutes to look at how that's unfolded.

On Thursday, in an interview published by Yahoo News he suggested that after the attacks in Paris, there would have to be greater surveillance of Muslims in the US.

He was then asked if that might require registering Muslims in a database, or crucially, presenting them with some form of identification card which listed their religion, in the words of the article.

He didn't rule that out.

"We're going to have to - we're going to have to look at a lot of things very closely," Trump said when presented with the idea.

"We're going to have to look at the mosques. We're going to have to look very, very carefully."

'A lot of systems'

Later that same day, an American network TV reporter asked Trump: "Should there be a database or system that tracks Muslims in this country?"

Trump replied: "There should be a lot of systems, beyond databases. I mean, we should have a lot of systems. And today you can do it.

"But right now we have to have a border, we have to have strength, we have to have a wall, and we cannot let what's happening in this country happen any longer."

The TV reporter pushed on: "But that's something your White House would want to implement?"

To which Trump replied: "Oh, I would certainly implement that. Absolutely."

The Trump campaign argued that Trump was "absolutely committed to a wall, not a database", suggesting that in the tumult of a campaign stop, the candidate misheard the question. 

But the reporter had followed up again and asked if the plan meant going to mosques to sign people up.

To that Trump replied: "Different places. You sign 'em up at different, but it's all about management. Our country has no management."

From that exchange, it's clear this was not about a wall.

Hillary Clinton and Bernie Sanders, two of the Democratic front-runners, predictably condemned the comments as did Republican rivals Jeb Bush, John Kasich and Ted Cruz.

But perhaps the most telling criticism came from the American Jewish Committee, which called the idea "outrageous and un-American".

Drawing parallels with Nazi Germany and the forced registration of the Jewish people, it said: "What Mr Trump proposes, in this case targeting all Muslims, is a horror movie that we Jews are quite familiar with."

No reverse gear

For Donald Trump, there appears to be no reverse gear. In the past when confronted with some of the outrageous things he said, there has been no apology, no retraction. 

At campaign stops he blamed the media, claiming the "bloodsuckers" were dishonest about things he said. 

When it came to refugees from Syria, he told one crowd of supporters, "I want surveillance of these people. I want surveillance if we have to and I don't care. I want - are you ready for this, folks? - I want surveillance of certain mosques, OK?"

Asked if he was not ruling out a database of all Muslims , he replied: "No, not at all."

At a rally on Saturday, Trump added a new line to his anti-Muslim rhetoric, claiming that after the attacks in New York on September 112001, he watched "news footage of thousands and thousands of people" celebrating the attack in Jersey City, New Jersey, "where" in his words "you have a large Arab population".

In a TV interview on Sunday, Trump insisted he had seen the footage and that to suggest he hadn't was simply being "politically correct", which, along with attacks on the media, is another Trump trope.

So the fact-checkers went to work. And no one could find any footage or any coverage of protests in the place and the time Trump described.

The police said it didn't happen. People in the area said it didn't happen.

At the time of the attacks, police rushed to the nearby town of Paterson where they heard there was a large gathering of men in the centre of the city's Middle Eastern Community.   

"When we got there, they were all in prayer," said the town's police chief.

The mayor of Jersey City tweeted his response saying Trump "has memory issues or willfully distorts the truth".

At his next campaign rally, Trump insisted his office had been bombarded with people calling "hundreds of people", saying they remember the pictures too.

The Washington Post checked out Trump's claims and could find anything to support him.

Apology demanded

Concluding Trump lied, its Fact Checker column wrote: "Trump has defamed the Muslim communities of New Jersey.

"He cannot simply assert something so damning; he must provide some real evidence or else issue an apology."

But with his crowds growing, his poll numbers rising and the possibility he may actually win the Republican nomination, Trump continues to defy expectations and to defy conventional wisdom.

The negative publicity seems to fuel the candidate and rile up his base support. It seems no matter what he says; his crowds don't care. 

The suggestion he's making up policy on the hoof doesn't seems to matter.

He continues to win support.

That's what continues to worry the Republican Party establishment and why Donald Trump is no ordinary candidate.