The first of four American presidential and vice presidential debates will be held tomorrow. In an election so far dominated by domestic issues, the debate season will give many voters their first real glimpse of the key foreign policy differences between the Republican team of Mitt Romney and Paul Ryan, and the Democratic ticket of Barack Obama and Joe Biden.
More than a decade after September 11, most of the electorate believes the United States should engage more cautiously in foreign affairs. This sentiment probably was reinforced in the minds of many US voters by the murder in September of four of their countrymen in Libya, and the protests in numerous Muslim-majority countries against an anti-Islamic film originating in the United States.
Perhaps the key exception to this cautious approach to foreign policy caution is Iran. Some polls show sizeable US public support for international efforts to prevent Tehran from developing nuclear weapons, even if that necessitates US military action.
Iran is just one of the international issues on which Mr Romney has articulated a more assertive posture than Mr Obama. Other examples include Russia, which Mr Romney has declared Washington's "number one" geopolitical foe. The Republican nominee has also accused China of stealing US technology and intellectual property, and of currency manipulation - with the implicit threat of sanctions should he become president.
Given the apparent differences between the two candidates, many international audiences are showing a keen interest in the election outcome. According to a Pew Global Attitudes Project report from June, more than a third of populations in countries as diverse as Britain, Germany, Jordan, Lebanon, China, India and Japan are either "closely" or "somewhat closely" following the campaign.
As in 2008, international polls tend to favour Mr Obama. But there has been a marked decline in international approval of his policies since he took office.
According to Pew, support in China for Mr Obama's policies has declined from 57 per cent to 27 per cent since 2009; in European countries including Britain, France, Germany, Spain and Poland, the average reduction in support was 15 percentage points (from 78 per cent to a still high 63 per cent); and in numerous key Muslim-majority countries (including Egypt, Jordan, Lebanon, Pakistan and Turkey), the average fall-off was 19 percentage points from an already low 34 per cent to 15 per cent.
At least part of the decline in Mr Obama's numbers was inevitable, inasmuch as international expectations about him were unrealistically high when he entered the White House. Two of the main international criticisms of his foreign policy (as was the case with the Bush administration's) are over-reliance on "hard power", and unilateralism.
Despite Mr Obama's withdrawal of US troops from Iraq, and his commitment to a similar pull-out from Afghanistan, there has been international criticism of his administration's use of unmanned drones to kill terrorists. In 17 of the 20 countries surveyed by Pew, more than half of voters disagreed with the use of drone attacks.
International support can only be expected to fall further if Mr Romney wins in November and follows through on his assertive foreign policy rhetoric. This could be amplified by the fact that he enjoys less personal popularity overseas than Mr Obama does.
A key question is whether Mr Obama and Mr Romney should care about what the rest of the world thinks. After all, no foreign citizens will vote in November.
The short answer is "yes".
Some in the United States completely dismiss the importance of international opinion. Such short-sightedness does not consider foreign policy cooperation and information sharing with Washington, both overt and covert.
Many of the foreign policy challenges facing the United States require extensive international collaboration, especially at a time of budgetary cutbacks. As key members of the Obama team, including Secretary of State Hillary Clinton, have asserted, cooperation depends on a better use of soft power (including diplomacy) and a more prudent use of hard power.
Combining hard and soft power more effectively - into what is now called "smart power" - was well understood by previous generations of US policymakers. For instance, Washington skilfully used both assets after the Second World War to cultivate support for a system of alliances and institutions, such as Nato, the IMF, the World Bank and the UN, that subsequently became a cornerstone of western success in the second half of the 20th century.
To be sure, today's world is very different from that of the Cold War. But the need for smart power endures.
Given the mood of the US electorate, the development of a comprehensive, coherent and well-resourced smart power strategy will not win many votes for either Mr Obama or Mr Romney in November. Nonetheless, this should be a pressing concern for both candidates if they are to fulfil their pledges to renew the country's leadership for a new generation.
Andrew Hammond is the former America Editor at Oxford Analytica, and a special adviser to former UK prime minister Tony Blair