After a series of controversial statements, underwhelming debate performances and a poorly reviewed Saturday Night Live appearance to boot, Donald Trump still remains at the top of the polls, confounding the political pundits who long ago predicted his campaign would crash and burn.

The Iowa caucuses, the first time Republicans begin to select a candidate, aren't until February 2016, meaning Trump and his policies and statements still have time to undergo far more scrutiny. But those aren't the only challenges Trump could face in winning the Republican presidential nomination.

1. No GOP establishment endorsements so far

The political history of presidential nomination races in both the Republican and Democrat parties teaches that the eventual candidate is one who has some, if not the majority of, backing from the so-called party establishment.

Former president Ronald Reagan, for example, had virtually no support when he made his unsuccessful run against Gerald Ford in 1976, but had managed to get some backing four years later when he won. Indeed, the last Republican to carry the party's nomination with little support from the establishment was Arizona senator Barry Goldwater in 1964, who went on to a crushing defeat at the hands of Democratic nominee and incumbent president Lyndon Johnson.

As for Trump, according to the statistical analytics website FiveThirtyEight.com, he has no endorsements from any Republican governor, senator or representative in the House.

While endorsements may not be a direct indicator of a candidate's chances of winning, they do serve as an indirect signal of the potential for candidates to consolidate support through donor connections and party officials in various states, says Geoffrey Skelley, a political analyst at the University of Virginia Center for Politics. 

"It's tough to see him winning without any support within the party," Skelley said. "I don't think you'd ever see a governor or senator endorsing Trump. Maybe one or two members of the House might."

"Basically, you can't take the endorsements in and of themselves as a sign that someone's going to win. But you can look at it as a signal of general support within the party and all that comes with that."

2. Party establishment could try to burn his candidacy

If Republican Party elders become concerned Trump has a real shot at winning, and that his nomination could cost the party the White House, they could launch a blistering advertising and ground campaign against him.

Or — in what might be a much more constructive approach — they could direct all their resources to one of the other candidates, says Julian Zelizer, professor of history and public affairs at Princeton University.

"Now they're splitting their money and time. But if they really focus in on one person, the establishment still has a lot of powers. You can read about endorsements everyday, you can see money really move in the direction of one candidate, and that often will create a dynamic that could shrink Trump's [lead]."

GOP 2016 Debate

The Republican establishment could coalesce around a candidate like Florida Senator Marco Rubio, left, to ensure Trump is defeated. (Jeffrey Phelps/Associated Press)

Nate Silver, founder of FiveThirtyEight, pointed out back in August that the Republican Party's delegate selection rules work in favour of establishment-backed candidates and against candidates like Trump. Delegates in some states are not formally pledged to the candidate who won that state, he noted, while about seven per cent of delegates to the Republican National Convention are party leaders.

"Much of the party's influence consists of what you might call 'soft power,' the ability to influence outcomes by persuasion rather than coercion," Silver wrote. "But the party also has some 'hard power': It literally makes the rules."

3. High poll numbers may not translate into votes

Trump may be leading in the polls, but it remains to be seen whether those supporters, some of whom have only just become politically engaged because of their attraction to the straight-shooting real-estate mogul, will show up at the primaries or caucuses to vote.

His support, according to polls, is quite broad, cutting across a large swath of the party but coming from more moderate Republicans, Skelley says.

"Who is more likely to show up in an actual Republican primary or caucus — someone who is a diehard committed conservative or very conservative Republican, or someone who is more moderate or has only become engaged because of Trump?" Skelley said.

"And you wonder if Trump's poll numbers slip a bit, does that end up sort of turning off the people who were supporting him who aren't typically that engaged in the process? Will they show up and vote? That's an open question." 

4. Trump's untested ground game and endurance

At a certain point, the Republican nomination race will turn into a contest of organization and not simply public relations, Zelizer says. That means Trump will need an extensive get-out-the vote ground game in all of the states to remain competitive. 

"As we get into Iowa and we get into New Hampshire and all the other primaries, you're going to need a very formidable grassroots organization to get him through those contests," Zelizer said. "He's untested at this point. He's hired some serious people in Iowa, but I don't know. Can he sustain that through the many primaries that are required to win?"

As well, Zelizer questioned whether Trump has the endurance to slog through the primaries and "deal with the day to day and very brutal process of campaigning in all these states."

GOP 2016 Debate

Trump would not necessarily receive the backing of supporters of Ben Carson, right, if the neurosurgeon were to drop out of the race. (Morry Gash/Associated Press)

"In the next stage, it gets much harder than giving some speeches and going on national television," Zelizer said.

5.  Ben Carson's support would move to Trump? Not necessarily

According to some polls, neurosurgeon Ben Carson, another so-called anti-establishment candidate, is about even with Trump at around 25 per cent support in the Republican race. It's possible Trump could pick up much of Carson's support if Carson were to drop out, meaning Trump could still be a force to reckon with even if the establishment coalesced behind another candidate.

But Carson's supporters tend to be more conservative, and come more from the evangelical base, than Trump's. It's not at all a given that those who support Carson, who first came on the national scene because of his opposition to Obamacare, would slide over to Trump, who has in the past praised the idea of national health care and tax increases.

"It's not clear [Carson's support] has the same kind of anti-establishment fervour," Zelizer said.