In particular, when he reaches Beijing next week, nothing will be able to disguise the fact that Mr Obama is paying a visit to his country's biggest creditor.
Those who take pleasure in America's discomfort point out that this global economic colossus has become shackled to the world's largest pile of international debt and pulled down by a sinking currency. By common consent China is the chief beneficiary of the financial debacle and a serious challenger to US hegemony.
Since economic might so often goes hand in hand with military strength, this shift in economic power, along with the recent weakness of the dollar, has been heralded as a harbinger of US national decline.
Neatly catching this mood was the title of Fareed Zakaria's recent best-selling book, The Post-American World And The Rise Of The Rest. Then came Mr Obama's reference in his inaugural speech to "a sapping of confidence across our land; a nagging fear that America's decline is inevitable, that the next generation must lower its sights".
Paul Volcker, former chairman of the Federal Reserve and an adviser to the president, chipped in with remarks in a recent interview with PBS, the US public broadcaster, that the rise of emerging markets was "symbolic of the relative, less dominant position the US has, not just in the economy but in leadership, intellectual and otherwise".
Central banks in the developing countries have rubbed salt in the wounds of the ailing giant. The Reserve Bank of India last week joined the central banks of China, Russia, Mexico and the Philippines in choosing to boost its reserves of gold in preference to dollar-denominated securities.
A veritable chorus of policymakers in countries running current account surpluses has declared that the reserve currency role of the dollar is unsustainable.
At which point, it is important to remember that we have been here before. Back in the late 1980s, Paul Kennedy of Yale University stunned the world's chattering classes with his assertion in The Rise And Fall Of The Great Powers that "the only answer to the question increasingly debated by the public of whether the United States can preserve its existing position is 'no'."
This downbeat verdict came around the time of the 1987 stock market crash, when there was continuing concern about the twin US budget and current account deficits.
The country had become an international debtor for the first time and was increasingly dependent on European and Japanese capital inflows. A supremely confident Japan was in the ascendant.
Declinist sentiment in the US came close to hysterical when Japanese companies snapped up New York's Rockefeller Center, Columbia Pictures in Hollywood and Pebble Beach golf course in California. "Who owns America?" demanded ABC News.
In one sense Prof Kennedy's thesis was right. As China, India and the other emerging markets catch up with the developed world, the US is bound to suffer relative economic decline in the shape of a falling share of lobal gross domestic product, even as it grows faster than most of the developed world's larger economies and remains the world's biggest economy in absolute terms.
Globalisation and domestic liberalisation have given these developing countries the chance to establish a share of global GDP commensurate with their size and history. Chinese economic performance before 1978 was, after all, an aberration viewed from the perspective of centuries.
In a study of leading economies, Angus Maddison of the University of Groningen has calculated that China's share of global GDP in 1820, before the industrial revolution in Europe gathered pace, was more than 30 per cent, which is well above the US's current share. A return to something more normal may thus be under way.
Where the Kennedy thesis appeared wide of the mark was in suggesting the US was seriously at risk of imperial overstretch, as with Spain in 1600 or Britain in 1900.
The more obvious case of overstretch in the 1980s was in fact the Soviet Union, which collapsed, while the US succeeded soon after in restoring its budgetary position under the Clinton presidency without a full-scale retreat from its international commitments.
The Japanese economic challenge, meantime, wilted as equity and property bubbles burst and deflation threatened. The US media's panic over the Japanese invasion proved a perfect, if inadvertent, indicator of a turning point.
The question now is whether the overstretch thesis was wrong or simply premature. Yet predicting the timing of the rise and fall of nations and economies is notoriously difficult.
Charles Kindleberger, the late economic historian, was one of many who believed that national vitality moved in a life cycle. Among the internal causes of decline he identified were increased consumption, decreased savings, resistance to taxation, inequality, corruption, mounting debt and finance becoming more dominant in the economy than industry.
Yet if this chimes with current circumstances, note that many of these things were also present in the US in 1929 when an earlier financial crisis coincided with the long transition from British to American economic hegemony.
When Kindleberger wrote his World Economic Primacy 1500-1990 in 1996, he believed the US was slipping. But he had no idea which country was likely to emerge as the next primary world economic power and regarded China as merely a dark horse for the role.
The most powerful argument supporting the declinist hypothesis concerns what Prof Kennedy called "the age-old task of relating national means to national ends".
Since there is a significant long-term correlation between productive and revenue raising capacity, and military strength, much hinges on the sustainability of fiscal policy. Here the omens are not good for the US.
Under the twin pressures of the financial crisis and the longer-term problem of ageing baby boomers, official projections point to budget deficits on an unprecedented scale.
The Peterson Institute for International Economics in Washington estimates that after nearing $1,500bn (€1,000bn, £905bn) in the current fiscal year - more than three times the previous record - the deficit is likely to remain close to an annual $1,000bn until 2020 or later.
Looked at from the perspective of the flow of funds in the economy, the counterpart to these deficits will largely be found on the current account of the balance of payments.
Here the institute reckons the current account deficit could rise from a previous record of 6 per cent of GDP to an awesome 15 per cent or more by 2030, equivalent to more than $5,000bn annually. It expects net external debt to rise from $3,500bn today to as much as $50,000bn, or 140 per cent of GDP, over the same period.
Such figures pose a daunting challenge for the Obama administration and a conspicuous threat to the dollar, since there is a huge overhang of dollar reserves in foreign hands.
From the end of 2000 to mid-2009 the International Monetary Fund estimates that official foreign exchange reserves rose from $1,900bn to $6,800bn, of which $2,300bn is held by China alone. More than 60 per cent of these reserves are in dollars.
Recent Chinese rhetoric, including a call for the replacement of the dollar as the world's main reserve currency by special drawing rights - an accounting unit used by the IMF in its dealing with its members -suggest a worrying loss of confidence in US monetary and fiscal policy.
At the same time Fred Bergsten, the Peterson Institute's director, argues that it is now very much in the US interest to reduce the role of the dollar and encourage a greater flow of reserves into euros, renminbi and SDRs.
Yet the threat to the dollar can be overstated. China is rattling the bars of a cage of its own making, since the reserves are a consequence of colossal intervention to stop its currency appreciating.
In effect, it is trapped in the economic equivalent of the mutually assured destruction described by theorists of nuclear deterrence in the cold war.
With exports amounting to two-fifths of GDP, it has been beholden to the US as borrower and spender of last resort in the global economy. And it cannot abandon the dollar without slashing the value of its own dollar reserves.
As for the potential of the Chinese currency to challenge the reserve role of the dollar, it may exist in the very long run but, in the absence of developed financial markets and a much stronger commitment to internationalise the renminbi, it remains pretty remote.
In fact, the weakest element of the declinist view of the US may be the high current estimates of the strength of the Chinese challenge. These have been elegantly punctured in a recent essay in foreign affairs by Josef Joffe, co-editor of Germany's Die Zeit.
China, he says, is a place where the rest of the world essentially rents workers and workspace at deflated prices and distorted exchange rates. Its export dependence, as well as being an economic Achilles' heel, has political consequences.
These include 70,000 civil disturbances each year that are not factored into the linear growth forecasts beloved of investment bankers.
China's demographics are unhelpful: it will, points out Mr Joffe, grow old before it grows rich. While on Goldman Sachs's numbers China will long have overtaken the US by 2050 with a GDP of $45,000bn compared with $35,000bn for the US, the median age in the US will by then be the lowest of any of the world's large powers except India.
Indeed, the US's working age population will have grown by about 30 per cent, whereas China's will have dropped 3 per cent.
Together with export dependence, this amounts to a huge challenge for Chinese policymakers in what is a very poor country. The US, meantime, still has an unmatched research and higher education establishment.
And in 2008 its military budget was $607bn, representing almost half of the world's total military spending. The military budget of China, so often touted as the next superpower, is less than one-seventh of that.
Nobody can gainsay the extraordinary achievement wrought by China in the fastest industrial revolution in human history. We are clearly moving towards a multipolar world and a multi-currency reserve system, in which US power will be more constrained.
Yet the US remains the most flexible of the large economies by far. History does not, except for Marxists, move on tramlines. If US policymakers rise to the fiscal challenge and Americans bring themselves to save more, there is every chance that the country will escape meaningful decline and remain the world's pre-eminent economic and military power for a long time yet.
That is a very big if. But for many people's money, the next generation of Americans will not be lowering its sights any time soon.
Copyright The Financial Times Limited 2009.