To outward appearances, little today is different: $6bn of spending has produced an unchanged Democratic President, a repeat of the last divided Congress and, it is confidently forecast, continued political dysfunction.

And yet something fascinating and profoundly hopeful has happened, too. Barack Obama's re-election was not only a triumph of campaign organisation and political resilience in an age of economic discontent, it stood as a victory for common sense – a reflection of what America truly is, rather than the fulfilment of a warped conservative vision that contradicts reality.

It was even a good night for two much-maligned bodies, the pollsters and the Electoral College.

The former called a close election exactly. The latter, an 18th-century anachronism, did precisely what it's supposed to do: translate a narrow majority of the popular vote into an unequivocal majority where it constitutionally matters.

Many are describing this as the "status quo election". There are fears that it comes as a mere prelude to a disastrous rush over the looming "fiscal cliff".

Listen to the mean-spirited, but now familiar, reaction of Mitch McConnell, leader of the Republican minority in the Senate, which only reinforces that impression: it was time for the President to deliver, he declared, "to propose solutions that actually have a chance of passing the Republican-controlled House of Representatives and a closely divided Senate".

In other words the same systematic House opposition to every proposal from the White House, and the same use of the filibuster to paralyse the Senate. Mandate, he might have asked, what mandate?

In fact, it is hard to believe that Congress and the President will not find a safe path down from the "fiscal cliff", a combination of mandated spending cuts and tax increases that will automatically take effect in January 2013. If not, economists warn, a fragile economy will be driven back into recession, amid the deepening eurozone crisis that helped send Wall Street tumbling yesterday. Did not Churchill note that, "We can always count on the Americans to do the right thing, after they have exhausted all the other possibilities"? Surely they will, this time too.

There are other clear upsides of Mr Obama's victory. For one thing, it ensures the survival of his healthcare reform, his defining legislative achievement. Obamacare is admittedly imperfect. But it is long overdue, bringing the US more or less into line with other rich countries that provide guaranteed coverage for all their citizens. His re-election also means that for the next four years American foreign policy, starting with a perilous showdown with Iran over its nuclear programme, will be in the hands of a leader of proven cool and sound judgement, who no longer has to worry about his next election.

That brings us to the most fascinating element of all: How will this supremely rational but sometimes over-didactic politician behave in his second term? Mr Obama's victory speech in Chicago on Tuesday night sounded uncannily like the electrifying keynote address to the 2004 Democratic Convention that launched him as a national figure, urging not a blue America and a red America, but the United States of America.

He must now live up to his words. Maybe, freed of electoral pressure, he will slip into the disengaged mode visible at the least successful moments of his first term. That would be disastrous. Vital issues remain, not least immigration reform and overhaul of the unwieldy and loophole-infested US tax code.

Mr Obama would do well to steal a leaf from Bill Clinton, his most effective surrogate during the campaign. That means massaging Congress, spending face time with its members, cajoling Democrats and Republicans alike. This is not the natural style of the 44th President, but it may be the best way of reaching a deal on reducing the deficit, the problem that almost forced a US debt default in 2011 and created the fiscal cliff.

Had Mitt Romney won on Tuesday, the can could have been kicked down the road. It may yet be: never underestimate the ability of politicians to stall. However a short window – perhaps two months – of real opportunity exists. A blueprint moreover exists, the bipartisan Simpson-Bowles plan that combines spending cuts, tax increases and the gradual scaling back of costly entitlement programmes. Mr Obama's refusal to embrace Simpson-Bowles was one of the errors of his first term.

But the biggest reason for optimism lies in the election's impact not on the winners, but the losers. Whatever Mr McConnell implies, Republicans suffered a massive defeat that extends far beyond Mr Romney's defeat. Republicans now face a stark choice: remake themselves, or risk becoming a permanent minority party.

They may have retained the House, where the Tea Party is the driving force and moderates have all but disappeared. But that chamber is a gerrymandered distortion. Ways have not yet been found to gerrymander entire states which elect individual senators, and there the results brook no argument.

Democrats had to defend 23 seats on Tuesday, the Republicans only 10. Yet Democrats actually made a net gain of one or two, winning in several states easily carried by Mr Romney. In the last two cycles, 2010 and 2012, excessively conservative (and poor) candidates cost Republicans at least five sure Senate wins. The lesson is clear: American voters are not in the market for the far-right candidates thrown up by primaries at which only the most committed vote.

Mr Romney started to do better in the campaign only in the later stages, when he moved towards the centre.

The Republican Party of the future must deal with the real America represented in the Obama coalition. It is a coalition of women, young people, Hispanics and other minorities, and urban professionals. If the white, male and ageing Republican Party continues to ignore this truth, it will be marginalised for decades.

Second time round: Hits – and misses

For the first time since James Monroe in 1820, Americans have given a third consecutive President a second term. Here are the last six incumbents who won twice.

George W Bush (re-elected 2004)

His second term was a near-unmitigated disaster. Iraq descended into chaos, Hurricane Katrina brutally exposed his lack of management skills. He left office amid the worst financial crisis in 75 years, with approval ratings in the low 30s.

Bill Clinton (1996)

His second term is remembered for the Monica Lewinsky scandal. But its achievements were notable, including a balanced budget. He left office with a 65 per cent approval rating.

Ronald Reagan (1984)

The Iran-Contra scandal overshadowed his second term. But in three summits with Gorbachev he paved the way for the end of the Cold War.

Richard Nixon (1972)

Nixon won a landslide victory, but resigned over Watergate just 21 months later. Early in his second term he signed a Vietnam ceasefire deal, but thereafter was destroyed by the scandal.

Dwight Eisenhower (1956)

The early verdict on Ike's second term was unfavourable. Much of it seemed to be spent on the golf course. In fact he kept America at peace, and enforced school desegregation.

Franklin Roosevelt (1936)

His second term was marred by strikes, a clash with the Supreme Court, and a crushing Democratic defeat in the 1938 midterms. Roosevelt won a third term in 1940, mainly on foreign policy issues.

Rupert Cornwell