How does Gordon Brown extricate himself from the quagmire in Iraq? It's the key question of 2007 in Westminster, as President Bush prepares to announce this week that he will be sending another 10,000 American troops to the Baghdad black hole.

Throwing good soldiers after bad might seem a sensible strategy if you are a Christian fundamentalist with a hotline to God. But for Brown this represents a huge moral and political problem which he will shortly inherit. The war is lost so what point is there in escalating the conflict and losing more lives?

British troops may be relatively remote from the forthcoming bloodbath in Baghdad, but British casualties will continue in the region. And we will be expected to give financial and moral support to whatever horrors are unleashed by Bush's last desperate throw of the dice. Worst of all, Gordon Brown will have to somehow behave as America's staunch ally.

I shudder at the thought of the first Bush-Brown summit in Camp David. The new British prime minister trying to be matey with the president is going to be stomach-churning. Do they share the same toothpaste? "Yo Brown"? I don't think so.

And how will Brown handle the joint press conferences in the White House briefing room? "Does the prime minister fully support the conduct of the conflict in Iraq?" What will Brown say? Will the new prime minister be able to support the war with that unassailable conviction, that maddening self-belief, shown by Tony Blair these last three bloody years? Surely not. It's not Brown's war, after all.

Despite all the assurances from Downing Street that he was fully signed up from the start, I simply don't believe that Brown would have gone into Iraq in the first place. If nothing else, the sheer cost of mounting an invasion in the Middle East would have appalled him. And Brown is much too clever to have gone along with the sexing up of intelligence reports to generate headlines about Britain being 45 minutes away from chemical attack.

And, while he accepts collective responsibility for the Cabinet decision to start the war, there is surely no way that Brown is going to accept personal responsibility for the deadly aftermath, the failure to plan for any civil administration, the disbanding of the Iraqi army, the brutality in Abu Ghraib and Fallujah. He has to show fresh thinking, if only to distance himself from the mistakes of the past.

In six months or so, Brown will assume the role of joint leader of the most disastrous foreign policy debacle since Vietnam. He is boxed in by commitments he has given to his predecessor, and he knows that if he steps out of line, Tony Blair will use whatever authority he retains as a former prime minister to attack him from the backbenches or the House of Lords. Just imagine Blair writing columns in the press disowning his successor for "undermining our armed forces and failing to ensure Britain's security against the threat of global terrorism". It could lose Brown the next general election.

So, how does he deal with it? Well, the good news is that the chancellor is, in some respects, rather better equipped to cope with the new situation than his predecessor - provided he has the courage to tackle it head on. No-one can accuse Brown of being anti-American. He goes on holiday to Cape Cod and has a large number of friends in America, many of them Democrat congressmen. And as fortune would have it, this is the party which now controls the US Congress.

Brown should find it relatively easy to strike up a relationship with the new Democrat speaker, Nancy Pelosi, who wants to see troop numbers reduced in Iraq, and whose legislative priorities include climate change and the national minimum wage. At last, political America is beginning to speak with a liberal voice again. By fostering good relations with Congress, Brown could realign British policy on the war without actually having to disown it.

Brown's long enthusiasm for devolution could also be a plus. The only credible political option for Iraq now is some form of home rule, under which the Kurds, Sunnis and Shias get political autonomy within a federal state. Devolution of power has been proposed by the former Iraqi defence minister, Ali Allawi, and at least gives an intellectual framework for Brown to work within.

Of course, devolution in a sectarian war zone is not an easy thing to achieve, as Northern Ireland has demonstrated. But this is the only show in town. It would require active engagement with the surrounding nations in the region - Turkey, Lebanon, Iran, Syria. Brown will no doubt try to mobilise some kind of common economic programme for the Middle East, lubricated by American money. Well, it's cheaper than a war which is costing $100 billion a year.

Brown brings a fresh mind to the problem of reconciliation. But even so, it is going to be desperately difficult to extricate Britain militarily from the Middle East, and more so from Afghanistan, where most of the British fighting is taking place and where most British casualties will come from. Devolution isn't going to cut much ice with the Taliban. Nor is the war-weary British public going to look favourably on continuing casualties. And Brown has a big problem here: his personality.

The chancellor lacks Blair's "empathy" skills - his ability to convey a sense that he feels others' pain, even when he has been politically responsible for inflicting it. Brown can be awkward and wooden in public and the danger is that he will convey a sense that he doesn't care about the continuing death toll.

For reasons which are not easy to understand, Blair has tended to be given the benefit of the doubt on Iraq. People seem to accept that his intentions were honourable. They may not be so sure about Brown.

And public opinion is rapidly turning against the whole Iraq venture. The black farce of Saddam's execution has been another of those defining moments in the tragedy. What better confirmation of the utter failure of the war than that it has turned Saddam Hussein into a martyr. The sight of Islamist militiamen taunting the dictator as he was hanged added a new dimension of disgust.

It's difficult to see how the British voters will accept further loss of British soldiers' lives in such a dismal cause. But Brown is locked on to the Bush doomsday device. It is going to make him or break him, and his fate will be sealed by the events of the next few months - events over which he has little say and no control.