NAMING yourself after the three-headed dog that guards the gates to hell was, perhaps, asking for trouble. Cerberus, the private-equity beast in question, now finds itself at the centre of a fierce debate about whether corporate America is in for a hellish time, as the credit crisis spreads from financial services to the rest of the economy.

Only months ago Cerberus was praised as the saviour of the American car industry when it bought Chrysler from its German owner and struck a remarkable deal with the unions to cut jobs and benefits. But on November 20th it emerged that Cerberus's bankers had abandoned efforts to sell $4 billion of the debt it took on when it bought Chrysler. Investors turned up their noses even when offered a 3% discount.

Cerberus has also been hit by growing problems at GMAC, the financing arm of General Motors, in which it bought a 51% stake for $14 billion last year. GMAC reported a net loss of $1.6 billion for the third quarter, up from a loss of $173m in the same period last year.

More controversially, on November 14th Cerberus pulled out of a $4 billion deal to buy United Rentals, a power-tool rental firm. This provoked so much criticism that the famously secretive private-equity firm broke its vow of silence, telling the Wall Street Journal that the attacks on its credibility and integrity were “unfounded” and that it still has “more than $10 billion of available liquidity”.

What happens to private equity may be a leading indicator of how the crisis in the financial system will affect the rest of the business world, both because private-equity deals are so dependent on large amounts of debt, and because many of the shrewdest judges of corporate value work for private-equity funds. The number of new private-equity deals has plunged with the financial crisis, and nobody expects activity to pick up again soon. The collapse of deals suggests that the business climate has changed sharply.

But how, exactly? Were the cancelled deals so marginal, and so dependent on cheap credit, that a relatively small rise in the cost of debt ruined them? Did Cerberus conclude that prospects for the American economy are now too bad to go ahead with the United Rentals deal? Does it see better uses for its capital elsewhere, in distressed debt, say? Is that $10 billion of liquidity really available? And is it really true that as goes Cerberus, so goes the rest of private equity, and the rest of business?

The only truly upbeat firms in America nowadays are the accounting giants, which for once are not being blamed for a financial disaster (this time that honour belongs to the rating agencies). They are determined to keep it that way, and are said to be racking up huge fees by challenging every assumption in banks' financial models to make sure they cannot be accused of optimism. The banks are thus having to disclose ever bigger write-offs, contributing to fear of recession in America both indirectly, by delivering a stream of bad news, and directly, by constraining banks' ability to lend (see article).

The reduced supply of credit is contributing to recessionary fears that are greater in America than in the rest of the world, because the American consumer faces an unusual combination of difficulties, says Ian Shepherdson of High Frequency Economics, a research firm. Fuel prices are soaring, house prices are falling, confidence is plunging and there are early signs that the jobs market is weakening, he says.

So far, the evidence that the credit crisis is spreading to other industries is more in the mind than in the data. For instance, most of GMAC's problems relate to its subprime mortgage lending, rather than defaults on car loans. But there are gloomy predictions about the outlook for consumer spending. Car sales are expected to be down from 16.5m last year to 16m this year, for example. The outlook for 2008 is even worse. Jerry York, a former GM board member, sees sales slipping to 15.5m, and Thomas Stallkamp, a former Chrysler president who oversees automotive investments at Ripplewood, another private-equity firm, expects something between 14.5m-15m. The lower figure would amount to the largest decline since 1991, when there was a full-blown recession.

There are other signs that stress is spreading, though it is not yet at recessionary levels—not least because corporate profits remain at record highs in America, and many firms have taken advantage of the years of plenty to get their balance sheets in shape. Even so, Home Depot recently said that it can no longer afford to continue with its share-repurchase plan. In the most recent survey of banks' senior loan-officers, 19.2% reported a tightening of lending standards to large and medium-sized firms, up from 7.5% three months earlier, and zero a year ago. Surveys of small companies suggest they are finding it harder to get the credit they need to grow.

Between June 12th and November 19th, the spread in interest rates between high-yield corporate debt and Treasury bonds doubled, from 2.6 percentage points to 5.2, says Ed Altman of New York University. The yield on high-yield bonds has risen to 9.33%, the highest level since 2002 and a sign of growing default risk, even though defaults remain near a historic low.

Mr Altman is especially worried by the large amount of low-quality debt issued in recent years, much of it to finance private-equity deals. Some 42% of high-yield corporate bonds issued since 2003 were rated B- or lower, rising to nearly 50% in the first six months of this year. Moreover, some $160 billion of leveraged loans are coming due next year. Refinancing them may be a struggle in today's financial markets.

Martin Fridson of FridsonVision, a research firm, has calculated that a severe recession (which, he stresses, he is not predicting) could result in a peak rate of between 16% and 20% of annual defaults on corporate bonds, far higher than in 1991. If so, lenders will retreat further and distressed-debt investors like Cerberus will be baying for blood. Businesses need lenders to finance their operations: they must be quaking at the prospect.