MONTREAL — By all accounts Prime Minister Stephen Harper will do more than just seek an extension of the current Canadian military engagement in Iraq next week.

The plan he will put forward in the House of Commons is expected to feature a more muscular mission that could explicitly leave the door open to Canada participating in airstrikes over Syria.

If only to avoid having the next deadline collide with the upcoming election campaign, the duration of the mission will be longer than the six-month period set for the previous instalment.

For better or for worse, after the next week, the positions of the three main parties will be cast in stone until after the election.

The Conservatives failed to secure any opposition support for the mission last fall.

So far that has done them more good than harm.

Canada’s military deployment in Iraq enjoys majority support nationally including — as a bonus to the government — in Quebec.

Past experience suggests that support for a military engagement inevitably erodes over time. Still it would likely take more than the few months between now and the October election for mission fatigue to truly set in.

Given all that, Harper is probably comfortable with the notion of again going it alone.

His strategists may even crave that possibility.

And yet, the prime minister would almost certainly reap more electoral rewards from crafting a parliamentary consensus on the mission than from turning it into yet another wedge issue.

On this as on their anti-terrorism bill, the biggest political risk to the Conservatives may be their own tendency to engage in rhetorical overkill.

Episodes such as the one that saw Defence Minister Jason Kenney put up fake pictures of Muslim women in chains on his Twitter feed to shame the opposition for voting against the mission are a case in point.

With memories of the previous Iraq and Afghanistan engagements still fresh in the country’s collective memory, more than a few voters start from the premise that this is an issue on which honest politicians can come to different conclusions as to the most appropriate role for Canada to play.

Polls show that Canadians — even as they are generally supportive of the military nature of the mission (as they are of Bill C-51) — are not looking to give Harper a blank cheque to lead the country in a ground war in the Middle East.

If the opposition has scored any points on the issue so far it has been on the perception that the prime minister has been economical with the truth about the combat exposure of the soldiers he so ostensibly confined to a training role.

On that basis prudence would dictate that, if only to avoid being blindsided by a significant development over the election campaign, Harper be as specific as possible as to what this renewed commitment might entail.

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But at the end of the day little would bolster confidence in the government’s case as much as the sight of some opposition cover for the Conservative position.

That’s partly why all eyes will be on Liberal Leader Justin Trudeau as take two of the debate over the Iraq mission gets under way next week.

There were mixed feelings within Liberal ranks as to Trudeau’s decision to vote against the mission last fall.

At the time some of the party’s elder statesmen made a more solid case for supporting Harper’s plan than their leader did for opposing it.

The Iraq debate coincided with the beginning of a slow but steady drop in Liberal support in voting intentions that now has the party tied with the Conservatives in most polls.

Against that backdrop, many have wondered whether Trudeau’s decision to support the government’s anti-terror bill earlier this year was a prelude to a reversal on the Iraq mission.

But one does not necessarily follow the other.

The Liberals could, for instance, have supported Canada’s military role in Iraq and opposed Bill C-51 instead of the reverse.

Indeed, some of their supporters wish they had gone that route.

But whether Trudeau sticks to his guns on Harper’s Iraq mission or reverses himself next week, he will have to do a better job of articulating his party’s position than he did last fall.

Chantal Hébert is a national affairs writer. Her column appears Tuesday, Thursday and Saturday.

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