AFP

THE Cannon building is the oldest of the mighty office towers that ring the Capitol, housing close to a hundred members of the House of Representatives with their retinues and a score of committee rooms. It is there, on Monday September 10th, that the latest battle in the long war in Washington, DC, over the conflict in Iraq, is to be played out.

This is a busy and consequential week for America's Iraq policy. Monday's hearing is an unusual combined sitting of the House's Armed Services and Foreign Affairs committees, to hear the testimony of the American commander in Iraq, General David Petraeus, and America's ambassador in Baghdad, Ryan Crocker. On Tuesday the two men will repeat the exercise before the Senate. And before the end of the week the administration is due to issue a written report on Iraq's progress towards a set of 18 military and political “benchmarks” which, if met, would signify that the country is ready to stand on its own feet. This report is likely to draw heavily, though not exclusively, on the opinions of the American government's two senior men in Iraq.

What was designed originally as a simple progress report has evolved into something far more significant: the Petraeus/Crocker testimony is being awaited almost as if it were holy writ. Yet both sides of the debate are preparing to draw opposite conclusions from whatever General Petraeus and Mr Crocker say. The president's supporters are determined to “stay the course” and leave Iraq only once victory of some sort has been achieved. The Democrats (and a fair few Republicans) now believe that the war is lost and that America should withdraw before it expends any more blood and treasure on a hopeless cause.

The witnesses may, of course, have a few surprises to spring, but the broad outlines are pretty clear. General Petraeus will note that the “surge”, which has seen an extra 30,000 men deployed in Baghdad and in Anbar province since February, has had a moderate degree of success. Sectarian killings have fallen sharply, weapons seizures are up, and fewer Iraqi soldiers and police have been killed—although attacks on Americans and American troop casualties have not abated much. In addition there has been, in part coincidentally but in part because of the surge, a virtual ending of the insurgency in Anbar province, once the most deadly part of the country, as ordinary Iraqis and their tribal leaders have turned in disgust against the foreign al-Qaeda killers in their midst. Much of this is an argument for continuing an active American involvement in Iraq.

But on the political front the news is much less good. The “benchmarks” report, when it is published, will show almost no progress towards a political reconciliation that could see Sunnis and Shias governing a united country together and sharing its oil revenues in an equitable manner. Which poses two very tricky questions. Is political progress possible if General Petraeus continues to keep the killing just about under control (though it is still, by any reasonable standards, appalling)? And if not, should America head for the exit, or does it have a moral duty to stay on in order to prevent the country slipping into full-scale civil war and bloodshed far worse than anything yet seen?

This is what Congress and the president will now have to decide. It is hardly an academic debate. The original reason both for the “benchmarks” report and for this week's hearings was a compromise between Congress and the president over a supplementary budget allocation for Iraq earlier this year: Congress was thereby putting down a marker that it would not continue to pay indefinitely without results. But the big battle over money is only just beginning. September 30th is the end of the fiscal year in America, and by then the main budget, including a defence request of close to $650 billion, needs to be passed. Congress is determined to end the war, using its power of the purse. The next few days will determine the shape of that struggle.