One of the most seductive elements of Barack Obama's ascent to the White House was his unshakeable conviction that he was being called upon, at a time of epochal peril, to bend the arc of history America's way.

Only a candidate possessed with such boldness and self-belief would have challenged Hillary Clinton for the Democratic nomination two years after leaving the Illinois state senate, promising in his first campaign speech to “transform a nation and usher in a new birth of freedom on this Earth”.

Only a man who frequently compares himself to America's greatest President, Abraham Lincoln, would declare that when he was elected, “the rise of the oceans will begin to slow”. Only someone who believes that America is on the crest of a dangerous historic wave - and that he “can help guide it” - would have undertaken a glitzy world tour midway through the campaign.

Such ostentatious gambles underscored his promise to transform US governance, and with his intellect and cool temperament made a combination many found thrilling.

In his first month in office he has pushed through an unprecedented $787 billion economic stimulus package, announced plans to save the car industry, stabilise the stricken banking sector and stem the flood of home repossessions.

Then came his near-$4-trillion budget last week. It is a manifesto to usher in a new age of government activism that involves levels of borrowing and spending never before seen in the US and is a document of such staggering ambition and risk that even some of Mr Obama's Democratic supporters are suddenly beginning to feel a little queasy.

A keen poker player, Mr Obama is gambling not only his own presidency, but the future wellbeing of the country. If he pulls it off, they might find room for him on Mount Rushmore. If he fails, he could bankrupt the world's largest economy.

There have been only a few watershed moments in US history, and this is one. In the face of such a dark economic crisis, Mr Obama believes that timidity will beget catastrophe. He believes that the peril of the moment compels him to tackle both the short and long-term financial problems all at once - and quickly.

What he unveiled last week was one of the most audacious agendas announced by a new president. He declared his intention not just to pump trillions of dollars into a short-term rescue for the economy, but also to press ahead with enormously costly plans to trigger a green industrial revolution, transform education and provide health coverage to all Americans. These are issues that have bedevilled Congress and other presidents for decades. Achieving just one would be an extraordinary achievement. Mr Obama wants all three - and fast.

What was most striking about the budget - including that it will explode the federal deficit to $1.75trillion this year, its highest since the Second World War - was that it was a ruthless declaration of how Mr Obama intends fundamentally to change the American social contract, from Right to Left.

Its goal is not just to rescue the economy. It is to crush conservatism, end the age of anti-tax, anti-regulation policies that have been the guiding philosophies of US governance for a generation, and usher in a fresh “epoch”, as his aides call it, of New Deal-Great Society wealth redistribution and central intervention that were repudiated by Ronald Reagan 30 years ago. Much of his agenda will be paid for by a ten-year, $1 trillion tax increase on families earning more than $250,000 a year, beginning in 2011, a move that critics say risks stunting the economic recovery.

Mr Obama and his aides are particularly attracted to the notion, put forward by the Yale political scientist Stephen Skowronek, that most of the truly transformative US presidents - and there are only a handful - followed failed ones. They include Thomas Jefferson after John Adams, Lincoln after James Buchanan, FranklinD. Roosevelt after Herbert Hoover and Ronald Reagan after Jimmy Carter.

Their belief is that these presidents were able to reshape, for at least a generation, the governing philosophy and electoral alignment because the public rejected the era that preceded them. Yet presidents who believe that they are governing at such transformational moments - as Mr Obama does - take bigger risks to achieve momentous change. The stakes he has placed on the table with his budget are extraordinary.

What has begun to trouble some even within his own party is that Mr Obama's pledge to spend the US out of recession, while slashing the budget deficit to $533 billion within four years, already looks recklessly optimistic. Few dispute, even among Republicans, the need for healthcare reform or to wean America off foreign oil. It is the scale of debt that Mr Obama is willing to incur to achieve these goals that is causing such heartburn.

And it is not just Americans who desperately need him to prevail. As Gordon Brown said in Washington this week, while pledging faith in the President's plans, everyone is watching the US economy. The entire developed world is banking on Mr Obama to succeed.

But much of his promise to rein in the deficit rested on a projection that the recession will cease and the US economy grow next year, but nobody can clearly see an end to this slump. The central question - how to stop the banking sector from collapse - is still a work in progress. They prefer huge injections of cash to stop the banks dying - but stop short of nationalisation - while they try to work out how to rid them of at least $2 trillion of toxic assets. There is still a significant chance that the scale of debt involved could devour Mr Obama's presidency.

The markets are so unnerved about Mr Obama's ability to rescue the financial sector, and by the numerous bailouts that have had little effect, that wealth is being destroyed on Wall Street at a rate not seen since the 1930s. The President said on Tuesday that he does not worry about “the day-to-day gyrations of the stock market”, but investors have made it clear that his economic prescriptions have so far failed to reassure them.

Mr Obama also says that much of his programme will be paid for by reducing the cost of the wars in Iraq and Afghanistan. Yet he has just ordered 17,000 more troops to Afghanistan for a war that his Defence Secretary says will be a long and difficult slog, and he is still groping for a strategy in Pakistan.

“We are always better off on the high wire,” David Plouffe, Mr Obama's campaign manager, said last year. Now Mr Obama is President, watching from below has become both enthralling and terrifying.