Is it the Iraq of George W. Bush, and, it seemed yesterday, of Iyad Allawi, the country’s Prime Minister: a military and political success story, a ravaged country moving inexorably, if fitfully, towards democracy, a mortal threat to Americans eliminated by the bold action of the US administration?

Or is it the Iraq of John Kerry, Democrats and most European political leaders: a quagmire for US troops, a country sinking into civil war, a breeding ground for international terrorism that is making Americans less safe by the day?

The answer to that question may well determine the outcome of the election on November 2.

For weeks, John Kerry has infuriated Democratic foreign policy specialists and political strategists with his failure to find the right approach to close out this presidential election.

Thanks in part to his own insistence on placing his military record at the forefront of his campaign and in part to a comprehensive hatchet job by Mr Bush at the Republican convention, the election appeared to be turning into a referendum on Mr Kerry’s character, a vote that, even some of his friends acknowledge, he would be unlikely to win.

The Iraq war was always likely to be the issue at the forefront of voters’ minds, but somehow Mr Kerry seemed incapable of exploiting popular unease about it.

His well documented journey through the highways and byways of circumlocution undermined his credibility on the issue. Over the past two years his stance — from support of the war to opposition, to support, and back again — meant any attack he made on President Bush would rebound.

But this week, under pressure from his foreign policy team to find a simple message and stick with it, and with the situation in Iraq itself looking bleaker than for many months, Mr Kerry finally decided to go for broke. In a speech in New York on Monday, he castigated the administration for what he called its catastrophic failure in Iraq. “Can anyone seriously contend that this President has handled Iraq in a way that makes us stronger in the war on terrorism?” Mr Kerry asked. “By any measure, the answer is no. Nuclear dangers are mounting. The international terrorist club is expanding. Radicalism in the Middle East is on the march. We have divided our friends and united our enemies. And our standing in the world is at an all-time low.”

His own plan for dealing with Iraq differed very little from Mr Bush’s, save some implausible claims that he alone will be able to get Nato and other allies to help out there. But aides have decided this matters less than connecting with an increasingly widespread view among Americans that Mr Bush’s war has failed and has made the country less safe. This assault on the President’s judgment and credibility, they believe, will outweigh any doubts the voters may have about Mr Kerry.

For Mr Bush, on the other hand, the political strategy for dealing with Iraq has been to avoid talking too much about the specifics; the US casualties, increasing insurgent attacks, kidnappings and so on. Instead, in his speeches he has referred to Iraq in general, abstract terms as a success and attempted to keep the political focus on Mr Kerry’s weaknesses.

The handover to Iraqis of national sovereignty at the end of June was, in this respect, a political masterstroke that enabled Mr Bush to avoid shouldering responsibility for the specific problems there subsequently. In his speech to the UN on Tuesday Mr Bush repeated his case that the war on terrorism and in Iraq in particular was transforming the Middle East for the better.

But as the situation in Iraq has become more turbulent, Mr Bush is in danger of seeming out of touch.

The picture he paints of a cheerful, sepia-tinted Iraq, of children returning to school and companies opening, looks at odds with the reality on the news bulletins. At times his blithe assertions can make him sound a little like “Comical Ali”, Saddam Hussein’s information minister, who insisted his boss’s regime was winning the war despite some powerful evidence to the contrary.

But for now Mr Bush’s aim seems to be to keep it that way. Yesterday, Dr Allawi in effect endorsed Mr Bush’s version of events and the President himself again insisted the war was a success. With just over five weeks to the presidential election, Republican advisers are keeping their fingers crossed that their version of Iraq will at least not be spectacularly contradicted by some new serious deterioration there.

After November 2, it may all be rather different. Washington has been abuzz with reports this week that the Pentagon is planning a renewed offensive at the end of the year against the insurgency, a concerted effort to take back lawless Fallujah and other Iraqi cities. As one former intelligence official said privately: “This has a start date of November 3.”

The Bush strategy seems to be to whistle a happy tune about Iraq while the election campaign is in full swing — and then quickly and aggressively acknowledge the difficulties afterwards. The question is whether conditions on the ground in Iraq will co-operate. Will they support Mr Bush’s version of events, or Mr Kerry’s?

Times Recommends

• 8,000 miles from Washington - Obama's grandmother
• Review: Oliver Stone's W in Beverly Hills
• Zimbabwe chaos wipes out education