'Look, if you've been successful, you did not get there on your own. When we succeed, we succeed because of our individual initiative but also because we do things together." So said President Obama, campaigning in Roanoke Virginia, last week. He went on: "If you were successful, somebody along the line gave you some help".

He listed great teachers, government research, roads and bridges and the whole fabric of the American system as various ways in which "somebody along the line" would have contributed to your success. This was the essence of the social liberalism of the great British thinker Leonard Hobhouse, but now championed by an American president. Hobhouse passionately argued that capitalist wealth was co-created by the interaction of society, social capital and the entrepreneur. Government investment, financed properly by taxation, was the precondition for a successful capitalism.

Fox News, self-appointed 21st-century American custodian of free-enterprise capitalism, rather as Pravda guarded communism, was on to the issue like a flash. In my New York hotel, I watched an overheated Fox commentator begin railing about socialism and before long Republican presidential candidate Mitt Romney took up Fox News' cue as is mandatory for any Republican politician. The speech really "reveals what he [Mr Obama] thinks about our country, about free enterprise, about individual initiative, about America," he declared. "Did you build your business? If you did, raise your hand." Hands, pre-arranged, shot up. "Take that, Mr President," he finished.

The slowest and most faltering economic recovery since the Second World War was already triggering anxious questions about how to regain American economic dynamism, but Romney's presidential candidacy has crystallised a fundamental debate about capitalism that will spill over into Britain. It is a potential turning point in both countries. For Romney, whose fortune was made at Bain Capital, the private equity company he co-founded, owned and ran, embodies all the ills (or strengths, if you are so-minded) of a capitalism dominated by financial engineering, with companies as casino chips. It proved Romney's downfall when challenging Ted Kennedy in the race for the Senate in Massachusetts in 1994. The Democrats are determined to make it his downfall a second time round. Bain Capital was, and is, a quintessential product of the 25-year boom in credit and asset prices that began in the early 1980s. Mr Romney spotted the opportunity. He would raise money from private investors, saying the aim was to deploy Bain's consultancy techniques on pre-established companies carefully bought for their turn-round potential. This, coupled with significant leverage, would guarantee sky-high financial returns, not least for Romney.

The public understands that if you finance buying a house with a bank providing 90% of the asking price, and the house doubles in value, then your own 10% stake multiples elevenfold. Romney would apply the same logic not to the wealth-generating activity of starting innovative companies but to buying existing companies. Banks were only too keen to lend vast sums of money for such schemes, as they did right up to the financial crash in 2008. The companies' own profits would service Bain's debt.

Bain Capital would make the company more valuable – taking production offshore to low-cost countries, selling off redundant land, slashing research and investment budgets. And the general rise in property prices would help matters still more. When the companies' profits had risen, they would then be floated on the stock market for a much higher price and, hey presto, everybody got very rich.

Private equity has always been controversial. A few mature and poorly managed companies have benefited from the private equity treatment, but it became a huge industry dedicated to deal-making, extravagant leverage and self-enrichment, leaving a trail of disasters in its wake. In Britain, EMI has been emasculated by Guy Hands's private equity fund and now looks likely to be swallowed up by Universal. American journalist Josh Kosman in The Buyout of America writes that many of the companies in the biggest PE deals in the 1990s fared worse than had the taken-over companies stayed independent. He identifies five companies – Stage Store, American Pad and Paper, GS Industries, Dade Behring and Details, all of which paid lavish dividends and fees to Bain before filing for bankruptcy.

For private equity is not at core about creating value through innovation and investment. That would need private equity owners to take another risk (the results from innovation are uncertain) on top of the leverage risk, hardly the point of the deal. Instead, the overriding requirement is to fatten up the company so it can be resold on the public markets to deliver great capital profits, just as Obama says.

Bain Capital is part of the problem, not the solution. The private equity recipe has ripped the heart out of innovative US while leaving its banks encumbered by massive non-performing debts. The business model is now broken and the US has to start to ask questions about whether the Bain type of allegedly individualist capitalism really delivers growth and jobs. As the answer is: no, what does?

Obama has begun the counter-argument. Innovation is necessarily about taking risks and unless there are mechanisms to share them between the private and public sectors, the risks and innovation are necessarily not undertaken. "The internet didn't get invented on its own," Obama argued. "Government research created the internet so that all the companies could make money off the internet."

He could have gone much further. The same is true of industries ranging from aerospace to pharmaceuticals. The whole ecosystem in which innovation is housed – patents, copyright, finance, universities, research, knowledge transfer, ownership rules, regulation to ensure common standards – is co-created between the public and the private. Innovative entrepreneurs and companies are in a continuous trial-and-error relationship with their customers, suppliers and outsiders, not isolated in an individualistic silo.

The Fox News charge that this is socialism is bewildering and dangerous nonsense. Anglo-American capitalism, mired in debt, low investment and out-innovated by its competitors in Asia and Germany, is at a crossroads. What is clearer than ever is that the conservatives' response is dumb. If Obama and the Democrats can beat them in the US it will have global ramifications – a chance to recognise what really makes good capitalism work. At last, it is game on.