Jonathan Pearlman With a wide triumphant smile, Australian Prime Minister Malcolm Turnbull marched through the stately grounds of Government House in Canberra, where the Governor-General had given royal assent to the newly passed same-sex marriage laws.

Asked by a TV cameraman how he felt about the end of the year, Mr Turnbull said confidently yesterday: "It's a great finish."

Mr Turnbull could be forgiven a moment of glee. He had just survived the so-called "killing season" - the final week of Parliament, in which embattled leaders in Australia tend to be ousted.

In recent weeks, there has been much speculation about whether he will be the latest Australian prime minister to be turfed out.

Mr Turnbull himself toppled former Coalition leader Tony Abbott in 2015. This followed Labor leader Kevin Rudd's ousting of Julia Gillard in 2013, three years after she unceremoniously toppled him in the first of Australia's recent - and destructive - series of political coups.

For the first time, opinion surveys have shown Mr Turnbull slipping behind Foreign Minister Julie Bishop as preferred prime minister.

Surveys also show the opposition Labor party has remained ahead of the Coalition since September last year. A Dec 4 Newspoll found that 53 per cent of people prefer Labor, compared with 47 per cent for the ruling Liberal-National Coalition.

These dire survey results have led to frenzied speculation about Mr Turnbull's future. But analysts question whether the Coalition will be willing to dump yet another leader, given that the recent trend has shown that internal party-room coups lead to only short-term gains.

Such coups present the government as unstable and leave embittered former leaders - such as Mr Abbott - whose continued presence in Parliament poses a constant threat to the prime minister.

The last leader to avoid being ousted - former Coalition PM John Howard - warned that it would be "madness" to dump Mr Turnbull.

"Another leadership change... would do very significant damage to the Liberal Party and government," Mr Howard told The Australian newspaper on Dec 1.

"The best option ... is to help make Turnbull's leadership succeed. In my view, he can still be successful."

But these final words seemed to recognise that, on his current course, Mr Turnbull faces defeat at the next election, due by 2019.

It has been a stark turnaround. A former merchant banker and self-made millionaire, the 63-year-old was once one of the country's most popular politicians, admired for his eloquence and mix of progressive views on climate change and social issues such as same-sex marriage, combined with more conservative views on economics.

But his standing has plummeted since 2015. Fearful of right-wing elements in the Coalition, he weakened his support for strong action on climate change and overcame his previous opposition to a national postal vote on same-sex marriage.

Last Friday, he announced a royal commission into the banking sector. This marked yet another embarrassing backflip for the pro-business PM, who had previously staunchly rejected the opposition Labor party's call for such an inquiry. But he was forced into the move by several rural-based MPs in his Coalition, who wanted greater scrutiny of the banks.

All this has occurred against the backdrop of the dual citizenship saga. So far, nine MPs have been forced to leave Parliament after it emerged that they held a foreign citizenship, which is barred by the Constitution. Numerous other MPs face questions about their citizenship status.

The saga was not Mr Turnbull's fault but as prime minister he appears to have incurred much of the blame.

Perhaps the strongest argument in favour of Mr Turnbull's leadership, say analysts, is that there is no clear alternative.

In a story headlined "Malcolm Turnbull can breathe easy: this will be a killing season without a killing", Fairfax Media commentator Peter Hartcher said that possible alternatives such as Ms Bishop have no intention of launching a challenge.

"They've seen the deep, enduring damage that a leadership coup inflicts," he wrote on Dec 2.

"If you want to replace the prime minister, you have to have a replacement. There isn't one, not yet."

And so the killing season ended with a joyful Mr Turnbull enjoying the legalisation of same-sex marriage - a historic change that prompted national celebrations.

He will survive into the new year, which will yet bring a further round of killing seasons.