This could be the week when the greatest financial crisis in history finally reached its nadir. Then again, it could merely be another week in which a brief rally in global stock markets has suckered more investors, politicians and commentators into assuming that the worst is over, when the tentative improvement in financial confidence is just another false dawn.

So which will it be? The answer depends, even more than usual, on the finance ministers and central bankers gathering at a potentially chaotic G20 meeting this weekend. The omens are not benign.

It is now understood that the global financial system can be stabilised and economic demand revived only through government intervention. Private businesses and consumers do not have the access to credit or the confidence to start spending and investing again. But government intervention will work only with some degree of international co-operation and that requires leadership from America. Yet despite the mandate won by President Obama, Washington has proved muddled in its economic priorities and indecisive in its financial response to the crisis.

International co-operation is necessary because of the global linkages of trade and finance. Any country that allows a bank to fail spreads financial contagion to every other nation. And any country that cuts taxes or boosts public spending or expands its money supply, creates demand not only for its own businesses and workers, but also for the world as a whole.

The upshot is that financial guarantees, fiscal stimulus and credit expansion, will be much more effective and less expensive for each country if they are implemented in a co-ordinated way. By contrast, imagine a global free-for-all, in which some nations subsidise their banks while others try to punish bankers; in which some central banks print money while others grumble about Zimbabwe and Weimar; in which some governments promise to spend their way out of recession while others denounce this as the road to perdition and call for belt-tightening in the public sector. Not only would such divergent policies cancel one another out at the global level, they would also deal another blow to confidence in the world financial system.

But how can global co-operation be achieved when governments around the world seem to have completely divergent economic philosophies and agendas for this weekend? Gordon Brown wants to close down tax havens, while the Germans want to regulate hedge funds, policies that may or may not be desirable, but which have nothing to do with the present crisis. The US is demanding that Germany, Japan and China announce new programmes of public spending and tax cuts - which is simply not going to happen, either this weekend or at the G20 summit next month. The financial markets, meanwhile, are hoping for a $500billion increase in the IMF funds available to rescue insolvent governments, but this does not seem a high priority for any of the G20 governments, except perhaps the Germans, who fear the cost of bailing out Latvia, Hungary, Austria, Greece and the Irish Republic will otherwise fall on them.

Past experience of such international negotiations shows that American leadership is necessary for reaching any kind of agreement. Which brings us to the greatest risk facing the world economy: Mr Obama's failure to present a credible response to the financial crisis or even to assemble a proper economic policy team. After the British Government's leaked messages of despair about nobody answering the phone at the US Treasury in the preparations for the G20, everybody is now aware that Mr Obama has nominated only two out of 18 deputy and assistant Treasury secretaries. What is less widely recognised is that this decision-making vacuum reflects a deeply worrying feature of US economic policy.

American politicians simply don't seem to understand the existential threat that their economy is now facing. Instead of uniting to deal with a national emergency far more threatening to their way of life than the terrorist attacks of 9/11, they have responded by dividing more sharply than ever into hostile partisan camps.

Efforts to revive economic activity and to stabilise the financial system that are clearly indispensable on the basis of any economic analysis, whether Keynesian or monetarist or plain business-sense, have been denounced on the Right for interfering with free markets and on the Left for feather-bedding bankers. Instead of rallying around in a moment of crisis, many Americans are openly expressing their hope that the new President will fail and the economy collapse. Candidates for key Treasury posts have been viciously attacked in the media and Congress for trivial tax and administrative infractions inadvertently committed many years ago or simply for having once worked on Wall Street. As a result, these jobs have become almost impossible to fill.

Mr Obama himself seems to have attached a surprisingly low priority to dealing with the financial crisis. He had, for example, selected key State Department officials, from Hillary Clinton downwards even before his inauguration. He has managed to get dozens of these confirmed by Congress in the past two months and immediately put his personal stamp on US foreign policy. Yet there has been no similar focus on creating a properly functioning economic team or launching a coherent new response to the financial crisis.

The lack of urgency, of focus and of national unity in America's response to the financial crisis is the most surprising - and most dangerous - threat to our chances of recovery. With clear American leadership, a global policy to stabilise the banks and pull the world out of recession could readily be agreed. All the main elements of such a policy - lower taxes, public works programmes, monetary and credit expansion, cast-iron government guarantees for recapitalised banks - are broadly agreed among economists and endorsed by global institutions such as the IMF.

None of these policies would be painful to voters, since they would involve easier financial conditions, lower taxes, more jobs and stronger guarantees for savings. Why then are they proving so hard to put into practice? Is it because many Americans would rather see their economy collapse than a Democratic President succeed? If so, then perhaps the Marxists now enjoying a new lease of life will have been right all along: American capitalism will have proved a decadent civilisation at the end of its global hegemony and doomed to self-destruction.

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