Now the wooing, enticing, cajoling - even coercing - begins.
Just as Turkey has faced intense pressure from the United States to allow the use of its territory for a possible war with Iraq, a half-dozen countries on the United Nations Security Council are about to begin feeling like the rope in a tug of war between two powerful camps.
The six, normally second- or third-tier powers on the diplomatic stage - Angola, Cameroon, Chile, Guinea, Mexico, and Pakistan - are the undecided Council members who are likely to determine the fate of two competing visions for Iraq.
On the one hand, the US, backed by Britain and Spain, will seek the six countries' support for a new UN resolution introduced Monday that would place an international imprimatur on the use of force to disarm Iraq. But also on Monday, France, Germany, and Russia began circulating in the 15-member Council their own proposal for enhancing weapons inspections as a way to put off war.
What comes now, officials and experts say, is at least two weeks of hard diplomatic sell as the US tries to convince a majority of nine Council members that weapons inspections have not worked. The new resolution is not expected to be voted on until perhaps mid-March - after chief UN weapons inspector Hans Blix updates the Council March 7.
Both sides in the battle will seek to isolate the opposing proposal by winning over as many undecided Council members - the UN equivalent of swing votes - as possible.
The objective, experts say, is to win the crucial battle for international public opinion.
"It's not a United Nations blessing of US action that we need. It's the support of domestic and international opinion, and going through the UN is the way we get that," says Ivo Daalder, a foreign-policy expert at the Brookings Institution here.
If the US is to fight a war with any country at its side, it will be only with a new UN resolution, Mr. Daalder adds. "[British Prime Minister] Tony Blair needs it for his domestic audience ... so does Spain, so does Italy," he says - and that means a Council majority of nine must be won over.
The White House acknowledges that while the US holds to its view that authorization for war is contained in previous resolutions - including 1441, which passed the Council unanimously last November - the new resolution is a concession to allies such as Britain that face strong antiwar majorities at home.
President Bush's national security adviser, Condoleezza Rice, told journalists Monday that "for a number of our closest allies [seeking a second resolution] was an important step to take." For that reason, she added, "It seemed a wise thing to do, and it does give people a chance to affirm, one more time ... the 18th resolution that calls on Saddam Hussein's regime to comply."
The critical line in the brief resolution states that "Iraq has failed to take the final opportunity afforded it in Resolution 1441," Ms. Rice says. The strategy agreed by the US and key allies Britain, Spain, and Italy, is to challenge the Council with such wording to simply affirm the action it took last November, officials say.
But right now the vote count is not in America's favor. Of the Council's four permanent and veto-wielding members besides the US, only Britain is on the US side. France and Russia are supported by China. Among the 10 rotating members, Spain and Bulgaria support the US, while Germany and Syria side with France. That leaves six to be courted like some newly discovered belles of the ball. And some observers say Pakistan may already be lost to the "yes" column.
What could make the Bush administration's work considerably easier are more signs of resistance to full disarmament by Saddam Hussein. Such evidence could come as early as Saturday, the Blix-set deadline for Iraq to destroy its Al Samoud 2 missiles, which inspectors say violate range capabilities set by the UN.
Iraqi officials on Tuesday said the UN demand was still being studied. But some experts - citing reports of stiff pressure on Baghdad from economic partner Moscow to show signs of cooperation with inspections - expect Mr. Hussein to accept the missiles' destruction as a PR coup.
"If Saddam is smart he'll destroy those missiles, and very publicly," says retired Admiral Stephen Baker at the Center for Defense Information in Washington. The possibility may explain why administration officials are repeating Bush's weekend comment that the missiles are "only the tip of the iceberg" in Iraq.
Brookings' Mr. Daalder says Hussein's decision on the missiles will set up Blix's March 7 report to the the Security Council as the key moment for the US-backed resolution. He notes that the six nations have sided with continued inspections in the past; what Blix reports could move them "one way or the other."