Is America in denial about the extent of its financial problems, and therefore incapable of dealing with the gravest crisis the country has ever faced?

This is a story of debt, delusion and - potentially - disaster. For America and, if you happen to think that American influence is broadly a good thing, for the world.

The debt and the delusion are both all-American: $14 trillion (£8.75tn) of debt has been amassed and there is no cogent plan to reduce it.

The figure is impossible to comprehend: easier to focus on the fact that it grows at $40,000 (£25,000) a second. Getting out of Afghanistan will help but actually only at the margins. The problem is much bigger than any one area of expenditure.

The economist Jeffrey Sachs, director of Columbia University's Earth Institute, is no rabid fiscal conservative but on the debt he is a hawk:

The debt is not a financial problem, it is a political problem David Frum, Former speechwriter to George W Bush

"I'm worried. The debt is large. It should be brought under control. The longer we wait, the longer we suffer this kind of paralysis; the more America boxes itself into a corner and the more America's constructive leadership in the world diminishes."

The author and economist Diane Coyle agrees. And she makes the rather alarming point that the acknowledged deficit is not the whole story.

The current $14tn debt is bad enough, she argues, but the future commitments to the baby boomers, commitments for health care and for pensions, suggest that the debt burden is part of the fabric of society:

"You have promises implicit in the structure of welfare states and aging populations that mean there is an unacknowledged debt that will have to be paid for by future taxpayers, and that could double the published figures."

Richard Haass of the Council on Foreign Relations acknowledges that this structural commitment to future debt is not unique to the United States. All advanced democracies have more or less the same problem, he says, "but in the case of the States the figures are absolutely enormous".

Mr Haass, a former senior US diplomat, is leading an academic push for America's debt to be taken seriously by Americans and noticed as well by the rest of the world.

He uses the analogy of Suez and the pressure that was put on the UK by the US to withdraw from that adventure. The pressure was not, of course, military. It was economic.

Image caption Many so-called "Tea Party" supporters fiercely oppose tax raises.

Britain needed US economic help. In the future, if China chooses to flex its muscles abroad, it may not be Chinese admirals who pose the real threat, Mr Haass tells us. "Chinese bankers could do the job."

Because of course Chinese bankers, if they withdrew their support for the US economy and their willingness to finance America's spending, could have an almost overnight impact on every American life, forcing interest rates to sky high levels and torpedoing the world's largest economy.

Not everyone accepts the debt-as-disaster thesis.

David Frum is a Republican intellectual and a former speech writer to President George W Bush.

He told me the problem, and the solution, were actually rather simple: "If I tell you you have a disease that will absolutely prostrate you and it could be prevented by taking a couple of aspirin and going for a walk, well I guess the situation isn't apocalyptic is it?

"The things that America has to do to put its fiscal house in order are not anywhere near as extreme as what Europe has to do. The debt is not a financial problem, it is a political problem."

Mr Frum believes that a future agreement to cut spending - he thinks America spends much too big a proportion of its GDP on health - and raise taxes, could very quickly bring the debt problem down to the level of quotidian normality.

'Organised hypocrisy'

I am not so sure. What is the root cause of America's failure to get to grips with its debt? It can be argued that the problem is not really economic or even political; it is a cultural inability to face up to hard choices, even to acknowledge that the choices are there.

I should make it clear that my reporting of the United States, in the years I was based there for the BBC, was governed by a sense that too much foreign media coverage of America is negative and jaundiced.

Image caption Are Alaskans fooling themselves about the viability of their state?

The nation is staggeringly successful and gloriously attractive. But it is also deeply dysfunctional in some respects.

Take Alaska. The author and serious student of America, Anne Applebaum makes the point that, as she puts it, "Alaska is a myth!"

People who live in Alaska - and people who aspire to live in Alaska - imagine it is the last frontier, she says, "the place where rugged individuals go out and dig for oil and shoot caribou, and make money the way people did 100 years ago".

But in reality, Alaska is the most heavily subsidised state in the union. There is more social spending in Alaska than anywhere else.

To make it a place where decent lives can be lived, there is a huge transfer of money to Alaska from the US federal government which means of course from taxpayers in New York and Los Angeles and other places where less rugged folk live. Alaska is an organised hypocrisy.

Too many Americans behave like the Alaskans: they think of themselves as rugged individualists in no need of state help, but they take the money anyway in health care and pensions and all the other areas of American life where the federal government spends its cash.

The Tea Party movement talks of cuts in spending but when it comes to it, Americans always seem to be talking about cuts in spending that affect someone else, not them - and taxes that are levied on others too.

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And nobody talks about raising taxes. Jeffrey Sachs has a theory about why this is.

America's two main political parties are so desperate to raise money for the nation's constant elections - remember the House of Representatives is elected every two years - that they can do nothing that upsets wealthy people and wealthy companies.

So they cannot touch taxes.

In all honesty, I am torn about the conclusions to be drawn. I find it difficult to believe that a nation historically so nimble and clever and open could succumb to disaster in this way.

But America, as well as being a place of hard work and ingenuity, is also no stranger to eating competitions in which gluttony is celebrated, and wilful ignorance, for instance regarding (as many Americans do) evolution as controversial.

The debt crisis is a fascinating crisis because it is about so much more than money. It is a test of a culture.

It is about waking up, as the Americans say, and smelling the coffee. And - I am thinking Texas here - saddling up too, and riding out with purpose.

Analysis is broadcast on BBC Radio 4 on Monday 27 June at 2030 BST and repeated on Sunday 3 July at 2130 BST. Listen again via the BBC iPlayer or download the podcast.