The grim task of recovering the bodies of those who perished in the terrorist attacks is likely to continue for quite some time. Throughout the American Union, this weekend will be one of mourning and introspection.
Nevertheless, the Administration knows that, as a new week begins, attention will overwhelmingly shift to the task of punishing the perpetrators of this crime. The US may currently feel vulnerable and traumatised, but it is far from losing its super-power instincts: if the country is "at war", as most of its politicians claim, then the nation expects a quick and overwhelming response, regardless of the fact that the enemy remains unseen.
A military operation is not in doubt; it will come sooner or later, and it will be fairly spectacular. However, President Bush is aware that an ill-conceived, botched military attempt will be worse than no action at all. He cannot repeat Bill Clinton's tactics when, in response to the destruction of two of his embassies in Africa, he fired off a large quantity of Cruise missiles at Afghanistan, only to discover that these managed to destroy a mosque and kill a few goats.
The sense of pain and revulsion inside the US has reached such levels that any similar failure would not only destroy the Bush presidency, but could also humiliate the entire US military machine for years to come.
Contrary to popular expectations, which predicted a similar kneejerk reaction, the Administration is carefully evaluating its strategies and is adopting small, measured and incremental moves. The calculation at each stage is that the operation must be regarded as a success, not only by ordinary Americans, but by the world at large. Mr Bush's fight is for credibility at home and abroad, in almost equal measures.
The list of available military options is as long as it is irrelevant.
Media pundits and ordinary Americans have an enduring love affair with the surgical strike, a single missile which miraculously pulverises an enemy thousands of miles away, by simply pressing a button from the comfort of a Washington general's chair.
The US military itself encouraged this idea during the Gulf War a decade ago, but most of Washington's planners know that it is a myth. Missile strikes can cause havoc to military installations and concentrations of troops; they are useless against scattered groups of terrorists.
At the other end of the spectrum of available options are the grand operations, such as carpet bombings and outright invasions. Yet, assuming that Osama bin Laden and his acolytes in Afghanistan are the targets now, it is impossible to believe that anyone in Washington would be considering such options.
Afghanistan has been bombed for over two decades by the Soviet Union and every conceivable band of local marauders to little avail; an invasion of the country was also attempted by the British empire and the Soviet one at different times, and both were ranked as abysmal failures.
Does this mean, therefore, that Washington has no viable options? Not necessarily, provided the US distinguishes clearly between short-term aims and long-term objectives, manages to dampen down unrealisable expectations and succeeds in creating a wider coalition of countries supporting its views. Success can never be guaranteed, but indications are that this is precisely what President Bush is doing at the moment.
The short-term objective is clearly to apprehend or kill those who masterminded the attack; the long-term aim is to eradicate terrorism. Apprehending individuals is very difficult but not impossible, as the growing success in capturing various Balkan war criminals over the last few years indicates.
Eliminating terrorism will remain, however, a dream for the distant future. Both objectives can be pursued in parallel, but each one requires very different military instruments, and a radically different approach.
The key to success in the immediate task of apprehending those responsible for this outrage is first-rate intelligence information, precisely what was lacking in Washington this week. The terrorists the world is currently facing are unique in that they operate at both ends of the technology spectrum at the same time.
On the one hand, they are able to fly aircraft and execute a murderous operation with a split-second precision which any military would envy. But at the same time they avoid modern-day communications, relying instead on fanatical internal discipline between small, disparate operational cells.
All Western intelligence agencies were configured at a time when the confrontation was between states. They are therefore good at intercepting communications, breaking ciphers or identifying command-and-control centres.
Since the end of the Cold War, intelligence agencies have devoted a greater share of their resources to following particular individuals, be they drug barons or terrorists. Yet even here, they often relied on following what in the military parlance is termed a "footprint", be that the transmission of a mobile telephone, the operation of a computer, or the tracing of an e-mail.
Israel managed to eliminate over the last few years many Palestinian leaders precisely because they left such footprints behind; in some cases, the mobile telephones which they operated actually guided the missiles which curtailed their lives.
Yet bin Laden's followers in general, and those who bombed the US this week in particular, never made this mistake. Acquiring information about them can only be accomplished by infiltrating their structures. This is a costly and risky operation which often requires years of hard work, one reason why most intelligence agencies attempt such efforts only with great reluctance.
And the task is much more difficult if those who are infiltrated must not only be of the same ethnic origin as the membership of the terrorist organisation, but should also appear to share a similar frame of mind, including an apparent readiness to commit suicide.
Again, this does not mean that the US must now start from scratch. American intelligence agencies were involved in covert operations around Afghanistan ever since the Soviets invaded in the 1970s. And, although terrorist attacks on US soil may be a novel development, Washington is not exactly a novice to anti-terrorist activities as such.
Furthermore, the US can rely on intelligence information from many other agencies, including former adversaries such as Russia, China and some Middle Eastern countries. Some of this information may be of doubtful quality, but it all helps to build up a picture fairly swiftly.
And, if bin Laden and his immediate acolytes are now the target, it is not necessary to identify the particular cave in Afghanistan where he may be spending a night in order to mount an operation.
A bigger slice of territory can be seized by special forces for a short period of time in order to apprehend him and his people, provided there are solid indications that he is somewhere in that zone. True, there will be casualties in the process, but America's 50,000 special forces routinely train for such operations, and the American public may well tolerate the price.
This is neither Vietnam, nor Bosnia, nor Kosovo, but an operation which is regarded by ordinary Americans as essential to their survival; provided it is crowned with success and the number of casualties is not vast, the old "body bags syndrome" is unlikely to hamper a US operation.
Much will depend on how the Administration defines success. It would be madness to say publicly that the seizure of bin Laden is the only objective. This is clearly the ideal aim but, even if a limited ground operation fails to take him out, the destruction of his headquarters or training camps can be touted as a victory, of sorts. The advantage of such small-scale operations is that they can be repeated; they neither raise the stakes too far, nor do they invite exaggerated expectations.
While the necessary intelligence is gathered and the preparations are made, the US Administration is currently using the time to build up a coalition of nations around its objectives.
From the purely military perspective, NATO's decision to regard this week's crime as an attack against the entire Western alliance is basically irrelevant. Washington's problem is not how to find the right military capabilities but, rather, how to deploy them effectively, a question on which NATO's other 18 nations are unlikely to have many novel ideas. Yet politically, NATO's support remains important.
It can persuade ordinary Americans that they are not alone. It also gives President Bush some necessary breathing space, as well as spreading the political risks of any future operation between many governments. And all the indications are that the Bush Administration is widening this strategy by including nations outside NATO.
A major success for Washington would be if some Islamic nations join this effort as well; this would give the anti-terrorist operation a more global dimension, and avoid the accusation that all we are witnessing is the traditional confrontation between the US and Islam, a supposed "clash of civilisations". The diplomacy currently being conducted behind the scenes appears competent, and promises encouraging results. But it is still fraught with many pitfalls.
It is not clear whether the Americans understand that, in return for enjoying the support of many Western countries, Washington would also have to consult them before mounting a military operation. The US is simply not used to making such concessions, and may be even less disposed to discuss its future military actions in the current climate.
Quite apart from the fact that discussions between 19 NATO member countries cannot be kept completely secret and secrecy is crucial to the success of any operation, there is also the problem that some NATO countries may object, as a matter of principle, to what Washington proposes to do.
So, the current consensus within the North Atlantic Alliance is wafer-thin, and may well shatter in the weeks to come. The best bet must be that, when the US does mount its operation, only a very small number of other countries will pledge their troops, while the rest of the world will simply look the other way, hoping that the storm will pass as the Americans vent their anger.
And this will not be a good basis for America's long-term objective, which is eradicating terrorism as such.
Whether they like it or not, US decision-makers have to face the unpleasant reality that millions of people in the developing world consider this week's events as "just punishment" for what they view as American arrogance. The US cannot change this overnight. Nor does it need to make concessions to fanatics; a small group of people bent on using violence will always exist.
But, while terrorism as such cannot be eradicated, it can be circumscribed, through a combination of active political engagement, aid programmes and a strengthening in the international legal regime. A good case can be made, for instance, that this week's atrocities should be classified as crimes against humanity, and that its originators and those who give them assistance should be subjected to the full rigours of both international and the national law of all states.
A stronger argument could be made that, faced with such crimes, the notion of the sovereignty of states no longer applies; a coalition of countries or international institutions should be authorised to hunt these people down wherever they are, just as pirates on the high seas or slave traders were two centuries ago, and just as Nazi war criminals were hunted down last century.
The snag here is that Washington has increasingly shied away from most of these measures. American foreign aid, although large, is puny in comparison to the country's national economy, and heavily skewed in favour of a few countries. It is also subjected to many political restrictions (such as abortion), which say more about America's internal politics than the real economic needs around the world. Successive US administrations have also rejected the jurisdiction of international tribunals.
Furthermore, as long as the US legal system continues to uphold the death penalty, courts in many democratic countries, including all of Europe, are likely to reject applications for the extradition of alleged terrorists to American jurisdiction. In essence, a long-term strategy against terrorism will require a major change in US posture and mentality. And this remains easier said than done.
The US is entitled to defend itself, and even to seek revenge for what has happened this week. But let no one believe that this is either the beginning of a new anti-terrorist regime, or an indication of a new international determination to tackle the root causes of violence.
Jonathan Eyal is director of studies at the Royal United Services Institute in London