Eight years later, candidate George W. Bush would warn that Clinton went soft on China, only to be in turn described as a "patsy" of Beijing as Barack Obama launched his own historic run for the White House eight years later.

Now Republican hopeful Mitt Romney is describing President Obama as a "near supplicant" of Beijing on everything from security to trade to human rights. Obama, meanwhile, is touting an unprecedented record of standing up to China over unfair trade while warning that Romney's private equity firm, Bain Capital, "shipped jobs to China".

When the pair squared off in Florida last Monday in their third and final debate, Obama described China as "both an adversary and a potential partner in the international community, if it is following the rules". It was one of the few insightful thoughts uttered in a segment on China that swiftly degenerated into squabbling over who-said-what-to-whom.

On one level, then, the 2012 race for the White House is a classic example of political blood sport. But across Washington, there are signs of an evolving debate about how a struggling US can keep its edge and leverage over a rising China. It is something that Obama and his leading advisers spend a great deal of time thinking about, according to White House officials. You just won't see it on the campaign trail, now in its intense closing stages.

Chinese diplomats in Washington know this only too well. Mention blustering campaign rhetoric and they roll their eyes before expressing quiet assurance that things will settle down to more measured statements once the circus is over, whoever wins.

On another level, however, there is no shortage of signs that the Sino-US relationship could be about to enter a more complicated phase, whether in the security or commercial spheres. Strip away the campaign bluster and there are hard issues that look set only to intensify once the race is over on November 6.

If Romney's momentum prevails and the Mormon former governor of Massachusetts enters the White House on January 20, he has - repeatedly - vowed to formally declare China a "currency manipulator" on his first day.

While such a designation may not necessarily bring immediate enforcement measures such as tariffs, it is widely expected to force a strong reaction from China's new leadership. A trade war between the US and its biggest creditor looms.

Obama and his team pounced on Romney's statements as further evidence that he is a loose cannon, warning that he risks boxing himself in with such hasty lines.

But listen closely, and they don't quibble with the sentiment. Obama talks extensively about his efforts to push China on the currency and level the trade playing field, pointing to successful cases brought before the WTO. And there will be more.

Both campaigns warn about the need to force Beijing to finally curb intellectual property theft, warning that it alone potentially costs an estimated two million American jobs.

Jeff Bader, one of Obama's key campaign advisers on Asia and a former senior official on his White House National Security Council, fleshed this out during a debate at a Washington think tank last week. Describing the threat of the "currency manipulator" tag as "important and useful", he said it was Romney's idea of doing it on the first day that was astonishing. "The Chinese leadership will retaliate … this I can guarantee," he said.

In reply, Princeton professor Aaron Friedberg, a Romney adviser, insisted the move would not bring "Armageddon". China, he said, was following a more coherent trade plan than the US and "we need to find ways to put leverage on China".

But it is not just trade. Both sides want to continue developing alliances and partnerships with China's neighbours and reject any notion from Beijing that this represents containment - even as they talk up engagement with China.

Bader said while Washington did attempt to contain the Soviet Union during the cold war, in no way was it containing China now. "No country has done more to help integrate China into the international economic system," he said of the US.

"Romney insists Obama has not been tough enough, and that his vaunted "pivot" back to Asia is under-resourced - particularly the number of ships he plans to base in the Pacific. Romney, however, has yet to detail how he would pay for what he plans to be one of the biggest naval expansions in decades."

Friedberg was blunter. If China was concerned at the way the US was being welcomed back to the Asian sphere, it "needs to take a look in the mirror" given its assertiveness in recent times.

Talking to administration officials, it is clear that US intelligence concerns over Chinese commercial involvement in sensitive communications, as well as cybersecurity, go far beyond the election cycle.

"Any suggestion that the recent action over firms like Huawei is merely election-inspired China-bashing is a misreading," said one top official. "There are very real questions across the highest levels of US security and intelligence establishments that will not be easily answered, no matter who wins next month."

A US congressional probe found that Chinese firms Huawei and ZTE posed a strong threat to national security.

Uncertainty about the path ahead is not limited to policy.

Even if Obama wins, his foreign policy team is heading for a shake-up, with Secretary of State Hillary Rodham Clinton planning to stand down after four years. Susan Rice, the ambassador to the United Nations, and veteran senator John Kerry, a one-time presidential candidate, are possible successors.

The questions loom much larger in the case of Romney. Washington foreign policy experts are struggling to figure out whether he is a realist - prepared to deal with the world as it is - or a more interventionist neoconservative.

His choice of national security advisers - and key potential figures in a Romney administration - offer mixed clues.

They range from former World Bank chief Robert Zoellick, to the hawkish Friedberg, and then to the arch conservative former Bush-era UN representative John Bolton.

Zoellick came up with the formula of nudging China towards being a responsible stakeholder in the international community; Bolton is known to treat international bodies with disdain.

"There is still a great deal about Mr Romney and his likely foreign policy that we just don't know," said Professor Robert Sutter of Georgetown University.

He said he expected the pragmatism of past administrations to continue, however, noting that while the American public - backed by the media and Congress - was wary of China, it did not want its leaders to create undue trouble in the relationship.

Whoever wins, one of the next administration's first challenges will be to deal with the so-called fiscal cliff - a combination of an end of tax breaks, tax increases and mandated spending cuts by the end of the year that some economists fear could tip the US back into recession.

US undersecretary of state Robert Hormats said he was aware of considerable interest in China over the issue.

"I think there is a growing sense in the US, among both parties, that something needs to be done to address these financial issues and be done very soon," Hormats said.

"The probability is that there will be a very intense discussion of these issues as soon as the elections have taken place … and I do think there is a good chance that a consensus can be reached to avoid a major problem recurring."

From the fiscal cliff, to concern about a new Beijing leadership to relations with its neighbours, one of the few certainties is that whoever prevails in two weeks will face an in tray marked "China" stacked high with problems and challenges from their first day in office.