Europeans are not alone in suffering a debt crisis. America has one too, which has led the ratings agency Moody's to consider cutting its AAA credit rating. At $14.3tn (£8.9tn), the US public debt, as a proportion of GDP, is the 12th highest in the world, and more than the UK's, Spain's or Portugal's.

But the size of the debt is not the problem. America can meet its obligations without much sweat. The question is whether it is willing to pay up. President Obama can raise more debt, raise more tax revenues, cut spending or, most sensibly, do a bit of all three. As you'd expect, the Republicans in Congress favour the third option. But they refuse to agree that the first two should make any contribution whatever, even though taxes are the lowest in 50 years. They also oppose cuts to defence, one of the two biggest items in the federal budget, and find public opinion so opposed to cutting the other – healthcare for elderly people (Medicare) – that some Republicans ran midterm election campaigns denouncing the cuts Obama had already made. If they persist in this position, America's creditors will not be paid and the richest country on the planet will be in default within weeks.

We may dismiss this as an example of America's dysfunctional political system and expect that, at the 59th minute of the 11th hour, the Republicans will cut a deal. But the American crisis is a dramatised form of the British dilemma highlighted this week by the Office for Budget Responsibility. It warned that, to meet the demands of an ageing population, taxes would have to rise by £22bn a year from 2016 – the equivalent of increasing VAT to 24%, or basic income tax to 25%.

You can imagine the fate of any government that introduced such rises. So is the answer to cut spending on elderly people? No, we don't want that either. "There is no evidence that the public wishes to see entitlements in later life reduce," said Michelle Mitchell, director of Age UK. No, indeed. They wish to see such entitlements increase.

The point is illustrated by responses to the Dilnot report on care for the old, published just before national attention was distracted by Rupert Murdoch and phone hacking. The report proposed that those with assets above £100,000 – a figure significantly higher than the present £23,250 threshold, and close to the median wealth for single women aged 75 to 84 – should continue to pay the costs of residential care.

But a lifetime ceiling of £35,000 should be set on what anybody has to pay, regardless of their assets. So you can own a £2m house – for which you will have no use if you are living in a residential home – and the state will pay your bills, at an annual cost of at least £1.7bn and probably more, given rising longevity. Food and accommodation would cost £7,000-£10,000 yearly, but most would find that from pension income.

This solution was warmly greeted by all shades of political opinion, particularly by Labour. The only complaints came from the Daily Mail – which seemed to think everything, including "hotel" costs, should be free – and, more mutedly, from the government, which didn't want to commit to the cost.

We may agree that a compassionate, humane and socially just society should look after frail, sick people at the end of their lives. But the Dilnot report is not about social justice or even, save for a few details, about the welfare of old people. The poor, who own no assets or very few, will not benefit. Old people will not receive better care; since the government will pick up more of the bill, the standard may fall.

The report is about preventing what it calls "asset depletion" – or, in plain English, protecting inheritances. The state will pay so that property owners need not sell unoccupied houses and can instead pass them (or the proceeds from selling them) on to their children who, as we know from studies of inter-generational mobility, are likely already to be affluent property owners.

This is all the more absurd when at least half of the nation's wealth is tied up in residential property, which has been an appreciating asset for most of the past 50 years and one that is more lightly taxed the more valuable it gets. Releasing some of that wealth seems unavoidable if we are to meet the costs of an ageing population.

Yes, the present system is unsatisfactory. Houses – buying, improving, paying back the mortgage – have formed the central lifetime narrative for most of the baby-boomer generation, some of whom struggled on modest incomes. To them and their families, the sudden and total loss of a hard-won asset seems arbitrary and unfair.

Labour floated a solution before the last election: a one-off compulsory "insurance" levy, payable by everyone at 65 or taken from their estate at death. The risk of needing care would be pooled, so that everyone would pay perhaps 10% of their assets instead of an unlucky few losing 90%. The details – whether the levy would be a flat sum or a percentage of assets, for example – were never resolved because the Tories shot the idea down, using the emotive and puzzling term "death tax" (what is wrong with a tax you pay only when you're dead?) and publishing pictures of gravestones. They got wide public support, as they did in 2007 when they proposed cutting liabilities to inheritance tax.

But if the cost of Dilnot is not to be met by a "death tax", where is it to come from? By levying national insurance on the over-65s, which would no doubt be called a "granny tax" and lampooned with pictures of old ladies subsisting on mouldy Cheddar? From increased general taxation? From means-testing disability benefits? From cutting other old folks' benefits, such as free bus passes? Or from increasing public debt? Put any of these to the vote and they would probably be turned down.

Britons and Americans like to think that, unlike spendthrift Greeks and Italians, they take debt seriously. Many American cities display "a national debt clock", recording daily fluctuations in public liabilities. But in both countries, public and politicians suffer from cognitive dissonance. They don't want the government to take on more debt, they don't want taxes to rise, and they don't want the state to stop spending on services, particularly for the old. By comparison, Mr Micawber was a model of sound housekeeping.