Each time events in Iraq reach some sort of turning point upon which an optimistic interpretation can be placed, as they did on Saturday, I hope that Mr Bush and Mr Blair will declare victory and withdraw American and British troops. They ignored the five previous milestones when such an announcement could have been made with a modicum of honour. The price of delay has been heavy in terms of loss of life, both of American and British troops and of Iraqi civilians killed by coalition forces.
They could have brought their troops home in June 2003 when complete victory over Saddam Hussein's forces had been achieved. A second exit point came up the following December when Saddam Hussein was captured. Then in June 2004, an interim government was formed with Iyad Allawi as prime minister. Legally, Iraq had become a sovereign country again.
A perfect moment to leave. Seven months later another opportunity came up when a 275-member national assembly was voted into power. Its task was to debate and approve a new Iraqi constitution. Mr Bush and Mr Blair could have said that a new Iraq was now in the making, but still they hung on.
Further exit points were reached in October 2005, when Iraqi voters approved the new constitution in a referendum, and three months later when a National Assembly was elected on an 80 per cent turnout of voters. This was progress, surely. Now there is a sixth opportunity for the Americans and British to state that they have done all that they can do and to leave.
Admittedly, the formation of Iraq's new government isn't a wholly reassuring event. But is it realistic to hope for an outcome that would resemble best practice in the western democracies?
At all events on Saturday the new prime minister, Nuri Kamal al-Maliki, unveiled his government, the first democratic administration that Iraq has ever had. Even so, outside the heavily fortified compound in which the Iraqi Parliament meets, it was another terrible day. At least 27 people were killed and the bodies of a further 21 Iraqis were found, having been murdered in earlier sectarian atrocities.
No wonder it has proved impossible to appoint ministers to the departments of the Interior, Defence and National Security. At the same time, key members of the Sunni parliamentary bloc walked out, among them hard-liners with links to armed gangs.
Nonetheless, Mr Maliki made a highly significant statement addressed to the Coalition. He vowed to improve Iraq's security forces so that US and British troops could conclude their task. He said he would try to "set an objective timetable to transfer the security mission to Iraqi forces, ending the mission of the multinational forces". Why shouldn't we take the Iraqi Prime Minister at his word and ourselves announce a timetable for withdrawal?
American and British commanders in Iraq would not be pleased so far as one can tell. In the very dangerous circumstances in which the coalition forces find themselves, they seem to be sustained by the noble idea that they are "holding the ring" or acting as "midwife" for the birth of a new democratic state. And they can see from their vantage points, as perhaps Mr Bush and Mr Blair cannot from the White House and Downing Street, how far Iraq is from the happy outcome for which they have been risking their lives.
They don't wish to hear that their sacrifice has been in vain. Of course they would obey orders and return home. But they wouldn't be able to say when they got back - "mission accomplished".
For Mr Bush and Mr Blair it is much worse. Hanging on in Iraq has become a nightmare from which they never seem to emerge. Their folly is staining their records in office. Whatever else they do or don't do, they must fear that they are fated to enter history with their names attached to a disaster.
They will be remembered with their predecessors in the halls of shame: Chamberlain and Munich, Eden and Suez, Johnson and Vietnam, Nixon and Watergate. They don't want to be next to figure in this series. That is why they obstinately pass by the opportunities to retreat. They want a better moment.
In fact, as each successive milestone has been passed without withdrawal of coalition troops, everything has become steadily worse. Iraq has now descended into a form of civil war. Wherever the three main communities of Kurds, Shia and Sunni live together, ethnic cleansing has begun. The minorities flee, the stronger groups fight for supremacy. At the same time, criminal gangs take their chances and carry out countless kidnappings. The middle classes flee to Jordan, Syria and Egypt.
On Saturday both The Independent and The Guardian published accounts by trusted correspondents on conditions in Iraq. They reached the same conclusion. In this newspaper, Patrick Cockburn wrote that the state of Iraq now resembles Bosnia at the height of the fighting in the 1990s. The Guardian described a vicious sectarian conflict rapidly spiralling towards civil war.
Meanwhile, Mr Maliki's government has to deal with unresolved issues. The interim constitution was approved only on the basis that the new parliament would make the final decisions on the role of religion in the new state, the division of power between central government and regional groupings and the distribution of oil revenues.
I can make a shot at describing what the final outcome is likely to be. Ethnic cleansing will run its course as it did in the Indian subcontinent in 1947, leading to the unexpected creation of a separate Muslim state, Pakistan. And as it did in the Balkans in the 1990s, leaving behind it the patchwork of tiny independent states that have replaced the old Yugoslavia.
Iraq will divide into three largely autonomous regions separating Kurds, Shia and Sunni from each other. Central government will be weak. Iran will exercise strong influence over the Shia areas. War lords and tribal chiefs will become mini Saddam Husseins. Nothing of value will have been achieved.
Can the continued presence of American and British troops make any difference to this outcome? It seems very clear that it cannot. They have not been able to prevent the descent into chaos thus far. Why should they succeed now?
One more forecast: Even so, Messrs Bush and Blair will not withdraw coalition troops except at the margins. For they cannot admit failure. Their periods in office are ruined. Their reputations are tarnished. In theory they could use Saturday's announcement of a new Iraqi government as a reason to get out. But they are trapped. And more lives will be unnecessarily lost before the agony is over.
The US President and the British Prime Minister really should be impeached, but I don't suppose they will be.