In accepting that the UN should have a security role in Iraq, President Bush has accepted reality.
Despite a recent claim by chief US administrator Paul Bremer that Iraq is "not a country in chaos and Baghdad is not a city in chaos", events suggest otherwise. Mr Bush does not want to get bogged down there.
The presidential election next year is a powerful incentive for the Bush team to consider any proposal that prevents Iraq from becoming a determining campaign issue.
US troops seek reinforcement
And the influential Congressional Budget Office (CBO), which carries out independent policy studies, has provided a practical reason for Mr Bush to change his policy.
It says basically that the United States does not have enough troops to do the job, especially if it needs to keep a substantial force free for potential action elsewhere. And the Korean peninsula is on everyone's mind these days.
The CBO report is in the form of a letter to veteran West Virginia Senator Robert Byrd, an opponent of the Iraq war.
It says that if the Pentagon continues with its current intention to rotate troops after one year in Iraq, it would need to reduce the 180,000 soldiers there now to between 38,000 and 64,000 by the winter of next year.
This would allow for family time, retraining and, above all, for enough troops to be kept ready for action elsewhere.
An alternative plan, to increase the size of the army by two divisions would, the report says, be very expensive. It would cost $19bn up-front and bring the cost of occupying Iraq to $29bn a year.
The idea of bringing the UN in was publicly floated by the Deputy Secretary of State Richard Armitage.
He is very close to the Secretary of State Colin Powell himself, and clearly would not have spoken without his chief's say-so. Mr Powell has now persuaded President Bush that this is the way forward.
Under US command
Senior administration officials have also restated what Mr Armitage stressed - that the multinational force would have to be under American leadership.
The concept is to set up a multinational force with an American general at the top carrying a dual responsibility.
He would command the whole force under a UN mandate but would also have direct control of US forces.
The force itself would bring in troops from countries like Turkey, India, and Pakistan - which have been unwilling to send them without UN approval.
After the bombing of the UN headquarters, though, such countries might be somewhat reluctant to send their troops in case they, too, become targets.
The UN would also be brought in much more on the political and civil side.
The arrangement was foreshadowed by the UN Secretary-General Kofi Annan.
Speaking after the bombing of the UN headquarters in Baghdad he said that "we have no interest in recommending UN blue helmets" but he did talk about "a multinational force that oversees the security arrangements with the UN focusing on the economic, political and social side".
France in particular is insisting on a major role for the UN which goes beyond the limited one offered in Security Council resolution 1483, under which the UN is subsidiary to the occupying powers.
French Foreign Minister Dominique de Villepin, who led the opposition to the war in the Security Council, said of this latest idea:
"The measures to be taken cannot simply be an increase or an adjustment of the current occupation forces. It involves putting in place a real international force under a mandate from the UN Security Council."
Britain, as chairman of the Security Council during September, is likely to play an important part in trying to get a new resolution through.
According to Iraq expert Toby Dodge at the University of Warwick in the UK, the proposal to involve the UN is all "too little, too late".
"The danger now is that diluting the US presence might not do the trick. The resentment against the occupation is so great," Mr Dodge said.
The bombing of the UN, he added, might also put off some potential contributors as the UN itself is now a target for the Iraqi resistance.
Mr Dodge told BBC News Online: "After the UN attack, a compromise is being thrashed out in New York. The fact is that the US needs others to come in with money and expertise.
"Paul Bremer, in a Washington Post interview, blew the ship out of the water by revealing that the costs of reconstruction will be huge and cannot be covered by Iraqi oil exports.
"So to get donors in, and there is a donors' conference in New York in October, they have to compromise. Colin Powell has seen that."