The large, puzzled-looking turkey President George W. Bush officially pardoned in a traditional ceremony in the Rose Garden on Monday is not the only American with special reason for gratitude this Thanksgiving.

Just like the one lucky bird who, every year, escapes his brothers' fate on the dining tables of American families, the Bush administration's foreign policymakers find themselves bemused by the speed with which events have gone their way in the last week.

The Taliban seems to be in terminal retreat into the backhills of Afghanistan; leading al-Qaeda figures have been eliminated, with the net tightening around Osama bin Laden; the Northern Alliance is making noises about its willingness to participate in a post Taliban government in Kabul; and the US-led international coalition has held together through it all.

There is little doubt that the pace at which these successes have been achieved has surprised the Bush administration. Though officials have pointed out that events have vindicated their military strategy, they acknowledge they did not expect the enemy to crumble as quickly as it has.

But more importantly, the sudden progress in what they have always said was only the initial phase of the war on terrorism is forcing important new decisions on Mr Bush's team rather sooner than they had expected.

The immediate challenge remains capturing Mr bin Laden. There has been much discussion within the administration over the past six weeks about the wisdom of making Mr bin Laden's apprehension a central objective of the campaign. Advisers wondered whether a target that might prove elusive was a wise one.

But since the successes of last week, the administration is again publicly committing itself to getting the al-Qaeda leader. Caution about the plausibility of hitting one man in an Afghan wilderness has been replaced by calm assertions that he will not escape.

The next big challenge, assuming the Taliban is forced out of its remaining redoubts, is what role the US should play in constructing a new government in Afghanistan.

Mr Bush, and his fellow conservatives in the Republican foreign policy establishment, have always been wary of extended US engagement in far-flung parts of the world. In the presidential election campaign last year, Mr Bush poured scorn on the Clinton administration's passion for "nation-building", and cited the disaster in Somalia in 1993 and the protracted engagement in the Balkans as evidence against US involvement in intractable ethnic and political conflicts.

Paul Wolfowitz, deputy secretary of defence, regarded by many as the intellectual leader of the modern conservatives, set out the case against US engagement in television interview on CBS at the weekend.

"We would like to see a stable Afghanistan afterwards, but that's not going to be achieved by the American military, and it's not even going to be achieved primarily by outsiders. In fact, one of the lessons of Afghanistan's history is if you're a foreigner, try not to go in. If you go in, don't stay . . . because they don't tend to like any foreigners who stay too long."

Others believe a deeper political engagement is inevitable if the kind of chaos that gave rise to the Taliban is to be avoided. The next, and biggest question, is where does phase two in the war against terrorism take the US?

Since September 11, there has been a simmering debate between, broadly, the Pentagon and the state department about the conduct of the war on terror - in particular whether to take the battle to Iraq. The dispute was settled by a provisional truce.

America-first conservatives at the Pentagon like Mr Wolfowitz, and internationalists, like Colin Powell, the secretary of state, agreed that the war against the Taliban had to be won before the question of Iraq should be reopened.

Now, state department officials point to the success of the coalition in helping the US and its allies conduct phase one of the war, and insist that an offensive against Iraq would shatter it, detaching even staunch allies such as Britain from the war.

But the supporters of an Iraqi offensive continue to argue that there were strong connections between Iraq and the September attacks, and they dispute the claim that, presented with evidence of Iraqi sponsorship of terrorist activities, Britain and other countries would not join a new offensive. And Pentagon planners are emboldened by what many see as a vindication of their approach to the war in Afghanistan - favouring an all-out assault against Taliban positions, against the state department's apparent reluctance to help the Northern Alliance to victory.

It is still not clear on which side of the debate Mr Bush and his key advisers will come down. But the moment of decision is getting closer.