Two weeks after President George Bush appealed for support from the UN general assembly, several security council member states, including France, Germany and Russia, remain firmly opposed to the proposed timetable for Iraq gaining sovereignty.
Their opposition has been bolstered by the UN secretary general, Kofi Annan, who believes that unless the resolution is amended it will not provide sufficient security for UN personnel.
None of the permanent members of the security council has threatened to veto the resolution. But if the council fails to secure broad support, abstentions will deprive the resolution of sufficient legitimacy as a mandate.
Failure to get consensus will not only dissuade other countries, such as India and Pakistan, from assisting, but also discourage donors of money worldwide.
The resolution calls for the US-led provisional authority in Iraq to retain ultimate control over the country. The Iraqi governing council, meanwhile, would draft a constitution, ratified by Iraqis, and arrange elections for a permanent government. That process could take at least a year.
Opponents of the American draft would like to see a quicker transfer of power to a provisional Iraqi government and for greater power sharing in the meantime.
This week John Negroponte, the US ambassador to the UN, told the security council that the resolution would not be significantly altered. Later he said: "What I told the council members was that if in the coming days we put forward a resolution ... they shouldn't expect any radical departures from the resolution.
"But it's certainly still our intent to press ahead with this resolution, and I think the preferred position would be to try to get a resolution completed, voted and approved as quickly as possible."
But few see much hope for the resolution unless significant changes are forthcoming, and Americans are now privately sounding resigned about it being rejected.
"We don't want to play this game for a long, long time," one senior administration official told the New York Times. "This is as much a choice for the council as it is for us."
Last week Mr Annan took the rare step of criticising the US draft for "not going in the direction I had recommended". Mr Annan is particularly concerned with the fate of UN staff after the bombing last month of the organisation's headquarters in Baghdad which left 23 people dead and more than 150 injured.
If the resolution is withdrawn it will amount to a diplomatic blow for the Americans, marking the second time this year that they have been forced to abandon a resolution on Iraq for lack of international support.
Withdrawal will also increase domestic pressure on Mr Bush, whose ratings have plummeted since his televised appeal to the nation for $87bn (£52bn) for the rebuilding of Iraq and Afghanistan.
The Bush administration launched a nationwide drive yesterday to regain momentum on the Iraq debate; Mr Bush is also planning to use his weekly radio slot to address the subject.
The diplomatic setback at the UN was offset by the pledge by Turkey's parliament on Tuesday to send troops to Iraq. But that move has provoked unease in Iraq's governing council, and outright opposition among Kurds in northern Iraq, where Turkish troops have previously tried to crush Kurdish militants.