As Tony Abbott wins support from the political class and commentariat, public trust in his Government's handling of international relations is actually falling, write Peter Lewis and Jackie Woods.

After a tough first year, the accepted wisdom is that the Abbott Government will stabilise its hold on power through its management of national security issues.

The way the horror of Islamic State is feeding back into domestic issues and the fact that the battle for the Ukraine has touched Australia so personally, means these two conflicts are not abstract geopolitics. We have skin in the game.

With bipartisan support under the stewardship of Abbott's best-performing minister, Julie Bishop, most commentators have accepted that these conflicts provide a platform for the Prime Minister to establish himself as the sort of strong national leader John Howard became in the wake of the Port Arthur tragedy.

After all, the 'rally-round-the-flag effect' - the popularity boost international crises can deliver - is an established political phenomenon.

The Coalition has been banking on this with all its political focus being on national security while the Labor Opposition attempts to maintain the domestic pain with focus on the vexed passage of the budget.

But this week's Essential Report casts the first doubts on this narrative. As Tony Abbott wins support from the political class and commentariat, public trust in his Government's handling of international relations is falling.

These figures show a drop in support since November when the new government was seen to be fumbling its diplomatic performance: turning back the boats and dealing with the fallout from revelations of spying on Indonesia's president and his wife.

While these findings are polarised between Labor, Coalition and Green voters, what is clearer is that the PM has failed to rise above the partisan fray.

Dig a little deeper and we get a sense of why he is failing to unite the nation: despite the bipartisan support within the Parliament and strong endorsement from what remains of the media, the Government has failed to convince the Australian public of its current course of action to support the US's limited intervention in Iraq.

Just 38 per cent of Australians endorse the decision to supply arms and weapons to Kurdish forces fighting the IS terrorists inside Iraq, with 36 opposing and a further 25 per cent undecided.

There is even stronger resistance for deeper engagement such as Australia sending military planes to support US air strikes in Iraq.

And on the issue of sending troops into Iraq, there is a sharp divide in support depending on who is coordinating the mission - with a split sample finding nearly double the support for a UN-backed intervention.

These findings suggest that while the insiders have agreed that something needs to be done now to stabilise the region, they have failed to convince a public who still equates Iraq with US-sponsored adventurism.

The stubborn refusal of the government's voting intention figures to improve may simply be a case of disbelief that a government that can scarcely navigate the politics of the Australian Senate could effectively navigate the torrid and complex conflicts playing out on the world stage.

But if this cause is as just and clear-cut as our leaders believe, a little more effort needs to be spent explaining the mission - the plan, the strategy and the dangers.

Perversely, the decision of the Opposition to back the Government may undermine this effort - without the contest of ideas, the government is being robbed of the forum to make its case.

It is in this context that calls from the Greens and Independents to debate the issue in the Parliament will likely serve both the national interest and the Government's political interests.

Because when it comes to Iraq, Australians expect more than a rubber-stamp.

The survey was conducted online September 5-8, 2014, and is based on 1,004 respondents.

Peter Lewis is a director of Essential Media Communications. View his full profile here. Jackie Woods is a communications consultant at Essential Media Communications. View her full profile here.