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It's more than 30 years now since Ronald Reagan asked the most potent question a challenger can ask when seeking to defeat an incumbent president: "Do you feel better off today than you did four years ago?"

Last night, Mitt Romney, in accepting the Republican party's nomination as challenger to Barack Obama, asked the same question -- knowing full well that for many American voters, in the midst of a prolonged economic slow-down, the answer is a resounding No.

Remember Sarah Palin, in that brief moment when it looked as if she might become the Republican party's standard-bearer? She used to ask the same question in a folksier, but perhaps even more potent, way: "How's that hopey-changey thing working out for ya?"

Because of course hope and change is exactly what Barack Obama did offer four years ago -- and for many American voters, the hopes of 2008 have become the disappointments of 2012.

As Mitt Romney put it last night: "Hope and change had a powerful appeal. But ... if you felt that excitement when you voted for Barack Obama, shouldn't you feel that way now that he's President Obama? You know there's something wrong with the kind of job he's done as president when the best feeling you had was the day you voted for him."

The US is still, despite everything, the biggest economy in the world. The man who sits in the Oval Office makes decisions that reverberate far beyond the US's shores. That's why, every four years, some people outside the US ask: "Shouldn't we all get a vote?"

The US opinion polls suggest that this year's election will be a close one. It's rare for presidents to be defeated after serving just one term (Jimmy Carter in 1980 and the first President Bush in 1992 are the most recent exceptions), but no one is taking it for granted that Barack Obama will still be in the White House next January.

It would be a different story if the rest of the world did have a vote, although it's true that national leaders are often far more popular overseas than at home (Margaret Thatcher was the prime UK example). According to one, 87 per cent of German voters, 86 per cent of French voters, 80 per cent of British voters, and 74 per cent of Japanese voters have confidence in Obama -- and large majorities want to see him re-elected.

Part of Mitt Romney's appeal to American voters is that he will be a tougher President than Obama. He believes, as he put it last night, that "when the world needs someone to do the really big stuff, you need an American."

He didn't mention Afghanistan or Iraq, but he did mention Iran, and he warned Russia and China that he'd be tougher on them too. (I couldn't help noticing, by the way, that he didn't once mention the last Republican president, George W Bush, who seems to have been almost entirely written out of the Republican history books, at least for now.)

It's often said that all that matters in any election is how voters feel about the economy -- and more specifically, about the economic future. In fact, it's more complicated than that, which means that despite the grim economic picture -- and in particular the jobs picture -- Barack Obama is still in with a chance.

For one thing, as Hillary Clinton learned during the Democrats' primary campaign four years ago, he's a supremely effective campaigner. He's also an inspiring speaker, which no one would claim for Mitt Romney. (Mind you, it may be that in 2012 there's less of an appetite for inspiration, and more of an appetite for perspiration.)

The electoral demographics may also be in Obama's favour: women voters, African-Americans, Hispanic voters, all lean towards the Democrats -- and the recent furore over a Republican congressman's remarks about "legitimate rape" will have done nothing to help Romney.

Next week the Democrats will hold their own convention, and after that, it'll be time for the televised presidential debates. I'll be watching, of course, and I'll also to be doing some reporting from the US in the run-up to the election in November.

I don't really want to bring down the curtain on the Olympi-bonanza before the closing ceremony's final firework has fizzled -- but we do need to remember that there's still a country to be run, even if it is half buried beneath an embarrassingly high pile of gold medals, and there's still a government that needs to run it.

And, as you may not have noticed amid all the excitement (a gold medal in women's taekwondo? Really? How did that happen? And when did horses start dancing to music?), the government is not a happy bunny. There will be trouble ahead.

David Cameron, as we discovered shortly before we went Olympi-mad, can't deliver on his promise to reform the House of Lords. This week, he gave up trying, which has greatly upset Nick Clegg, who in return says he now won't support proposals to reduce the number of MPs in the House of Commons, which would have been a great help to Mr Cameron.

Remember when we were governed by the TB/GBs? (TB=Tony Blair; GB=Gordon Brown.) Their hate-hate relationship poisoned the machinery of government and did none of us any good. Well, now it's the DC/NCs (DC=David Cameron; NC=Nick Clegg.) Maybe they don't hate each other in that fratricidal way that Blair and Brown did -- but they've certainly fallen out of love.

The lovey-dovey of the Downing Street rose garden in May 2010 is no more than a distant memory. The trust has gone, and neither of the coalition partner leaders believes any more in the ability of the other to keep his promises.

We are not yet half way through what is meant to be a five-year term for the coalition government, yet I sense increasingly that ministerial thoughts are already turning to electoral calculation. The Tories desperately want to win a majority that would allow them to govern without having to rely on those pesky Lib Dems -- and the Lib Dems desperately want to avoid annihilation.

Restive Conservative backbenchers seem to be chafing unhappily from the constraints of coalition, and when they look at what the opinion polls are telling them, they conclude that voters are no longer impressed by their protestations of coalition compromises in the national interest.

So what are they going to do about it? Do I think David Cameron is about to be overthrown by a phalanx of toga-wearing Boris Johnson centurions chanting blood-curling threats in Latin? Of course not. Do I think the Lib Dems are going to throw Nick Clegg to the wolves, in the hope of being able to appeal to the electorate in 2015 without a Clegg albatross around their neck? Er, unlikely, but not impossible.

The point is this: even if you care not a fig for the machinations of Westminster, these guys are responsible for devising policies that may, perhaps, help the UK economy out of the doldrums. If they are at each other's throats all the time, and looking for opportunities to do each other down, it doesn't exactly bode well for the rest of us.

Perhaps you haven't noticed, but the euro crisis is still very much with us, even if most of the bankers and traders are on holiday at the moment, and the latest figures on the UK economy (zero growth predicted for 2012, the trade gap at record levels) are pretty grim.

So although much of the country seems to have thoroughly enjoyed the combination of a bit of sunshine and an unexpectedly successful Olympics, it's a pretty safe bet that it won't take long for the smiles to fade. And I'm not expecting to see many smiles on the faces of Mr Cameron or Mr Clegg.

I know the marriage metaphors have been overdone, but I can't help observing that the prime minister and his deputy do look increasingly like a couple trapped in a marriage that's no longer working. If they stay together, it's because they think they'd be worse off separately -- but that doesn't stop them dreaming of it every night.

My colleague Mark Easton, the ´óÏó´«Ã½'s Home Editor, has written a thought-provoking piece today in which he reflects on the very different national mood from a year ago, when several English towns and cities were engulfed in riots.

In his words, we've moved on "from national soul-searching to national celebration in exactly 12 months; from Broken Britain to Team GB."

So how come? Are we the same people, burning down shops in the High Street one minute, then cheering on Jessica Ennis, Mo Farah and Bradley Wiggins, plus our rowers and jumpers and gymnasts, the next?

A couple of random thoughts for you: first, wouldn't it be interesting to track down some of the rioters from a year ago and ask them if they're as swept up by Olympic-mania as the rest of us?

And second, perhaps we're a nation of teenagers, subject to extreme mood swings. One moment, it's all: "I hate you, you've ruined my life"; then it's "I love you to bits, you're the best."

We wept over the death of Princess Di; we cheered the wedding of Wills and Kate; then we did a spot of rioting, and now we're glued to the telly-box marvelling at the achievements of Team GB.

Emotional spasms, or a nation so diverse in its make-up that it encompasses all the above, and more?

So here we are, one week in, and I'm still trying to get my head round all this Olympics stuff. What I can't quite work out is whether I am meant to be celebrating astounding individual achievement -- that unique combination of skill, training, dedication and sacrifice that makes a champion -- or national prowess, marked by hoist flags, muttered anthems and gold-plated medal tables?

In other words, am I saluting Bradley Wiggins and Chris Hoy and Helen Glover and Heather Stanning -- or (at time of writing) five golds, six silvers and four bronzes?

The making of Olympic champions is a mysterious business, isn't it? After all, why are the two nations at the top of the national medal table -- China and the US -- about as different as two countries can be when it comes to the relationship between the individual and the collective, yet both, it seems, equally good at turning out medal-winners?

And why is it that the world's two most populous nations, with two of the fastest growing economies on earth -- China and India -- should have such very different Olympic achievements to their name?

As of dawn this morning, China was top of the London 2012 medal table with 18 golds, 11 silvers, and five bronzes -- and India was at number 41 with, er, one bronze. (Four years ago, in Beijing, India did get one gold -- to China's 51 -- in air rifle shooting.)

As it happens, this hasn't been India's week. Not only has it seen China yet again sweep up the Olympic medals as if they were chocolate buttons, but it has suffered the shameful embarrassment of two successive days of disastrous power failures that left up to 600 million people without electricity.

Failed traffic signals, stranded Metro trains, miners trapped underground, hospitals running emergency generators -- it's not exactly the picture India would like to present of itself as a thriving, entrepreneurial economy with a booming private sector and a rapidly expanding middle class.

(Mind you, there are plenty of Indians who know only too well what it means to live without electricity day in and day out. As the spoof headline in the American satirical publication The Onion put it: "300 Million Without Electricity in India After Restoration Of Power Grid." Think about it.)

But I digress. What does it take to make an Olympic champion? On the individual level, clearly you need talent, dedication, a good coach, and a willingness to put your life on hold, if necessary for several years, to reach the heights of Olympian success.

It also helps if you are privately educated: as the chairman of the British Olympic Association, Lord Moynihan, pointed out yesterday, half of the UK medal-winners in Beijing four years ago went to private schools -- something he described as "one of the worst statistics in British sport".

On a national level, you need a structure designed to spot talent early, nurture it, train it and finance it, perhaps to the tune of many tens of thousands of pounds per individual, until that peak of perfection is reached.

In totalitarian states like China, or North Korea, or the old Soviet bloc, it was easy -- you just plucked likely candidates from their kindergartens at an early age and groomed them for athletic stardom. In freer societies, it's more difficult, although as the US has shown, still perfectly possible. The lure of millions in corporate sponsorship can be every bit as persuasive as a Party official.

I spoke this week to a leading Chinese broadcaster who argues that it no longer makes sense for a country like China to obsess about its medals haul -- that as a nation well on its way to becoming the world's number one economy, it no longer needs Olympic glory to persuade the world to take it seriously.

Yet perhaps as long as there are nation states, there will always be a need to encourage national pride. If we no longer charge into war brandishing flags, perhaps it is better that we aim for sporting triumphs instead.

The answer to my original question, I suppose -- do we celebrate the individual or the nation? -- is that we are meant to celebrate both: the winning athlete who bears the flag aloft, and the flag itself, as a symbol of who we believe ourselves to be.

So here's another question: if Team GB acquit themselves with valour, and if London 2012 is deemed to have been a great success, what, if anything, will we have learned about ourselves as a nation?

I suggested before the Games began that we might feel happier if the whole thing turned into a bit of a damp squib -- that the national psyche is tuned more to failure than to success. Now, I'm not so sure. Do I detect a muttering? "Hey, maybe we're not so rubbish after all ..."