Will a “surge” of US forces help to secure victory in Iraq for President Bush? It is hard to see how it could, although American officials emphasise that, if Mr Bush does announce that he will attempt one last push, it will be much more than simply flying in more troops.

The weakness in the plan is that it assumes the Iraqi Government wants the same as the United States: a multi-ethnic country, with power shared between factions. But there are many signs that it does not; in that case, buying it more “breathing time” will be a waste of effort.

As Mr Bush prepares to reveal his decision, the most significant of the rest of his presidency, he is surrounded by advocates for a dozen conflicting theories. But he has no support, other than from some close aides, for what is thought to be his preference: a surge of more troops. The new Democrat-controlled Congress, which gathers today, is against it; so are many in his own party, while military commanders have been sceptical.

It has taken a lot to separate Mr Bush from General George Casey, the commander of coalition forces in Iraq, but the past two months have done it. In sacking Donald Rumsfeld after the November congressional elections, Mr Bush opened the door to military criticism of the Secretary of Defence’s handling of the war.

Mr Rumsfeld, who had worked particularly closely with General Casey, cutting out General John Abizaid, commander of the US Central Command, and others in the Pentagon, had defined success by the state of security, and had held back from turning over provinces to Iraqis. Mr Bush said many times that he would give General Casey all the troops he needed.

Since those tactics failed to bring Baghdad under control — acknowledged by Mr Rumsfeld in a memo in the week of his departure — those who want to hand over provinces to Iraqis, despite the risk of violence, have won more influence. General Abizaid has long been a proponent of this; General Casey, who is due to leave his post soon, has moved closer to this position, officials say.

However, Mr Bush is loath to adopt a plan he equates with defeat — hence the speculation that next week he will announce a last surge. If he does, there will be an argument about numbers; even 30,000, for six to nine months, would be hard to muster, one official says. Army officials fear the effect on recruitment and retention if troops are sent back for more tours of Iraq than they had expected, or are denied the customary period at home between tours.

Nor is there agreement on what a surge should do. More troops might make Baghdad a little quieter, for a bit, with the aim of giving the Government a “breathing space” to regain control. There may also be more money, and a drive to create more jobs, to boost the popularity of the Government, says one official.

But many speculate that the insurgents would simply wait until the US forces left, while taking advantage of their presence to send casualty rates even higher. The US may try to embed more troops with the Iraqi Army to “influence” rather than do the fighting itself. But this risks making them hostages, and their ability to get the army to crack down on Shia militias is also in doubt. Nouri al-Maliki, the Prime Minister and a Shia, has blocked previous attempts by US “embeds” to do this.

Iraq’s greatest problem is the sectarian violence of Shia against Sunni. The United Nations estimates that 100 Iraqis have been killed a day recently; other estimates put the numbers fleeing the country at 60,000 to 90,000 a month.

The US has been frustrated at the inability of the Shia-led Government to end the violence. But that is generous to the Shias in Mr al-Maliki’s administration. They may not share the US goals of allowing the Sunnis a real stake in power, whatever they say to the contrary, and will tolerate or even encourage their persecution. Even the Army, often held up by the US as one of the more solid achievements, has become predominantly Shia and Kurdish, and its impartiality cannot be assumed.

Bush’s desire not to withdraw is understandable. But as he debates whether to risk a surge, a commitment that would leave him extraordinarily isolated at home, he needs to decide whether the Government in Baghdad really shares his aims. If it does not, then he is wasting US troops’ lives.

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