A view shows newspapers with Barack Obama winning the US presidential election on their frontpages, at a news stand in Times Square, New York.

Barack Obama has been called many things since he first started campaigning for president. To his extremist opponents he is a Muslim, socialist, and Kenyan. (Sometimes all three at the same time.) To his supposedly mainstream critics, he is incompetent, impersonal, and impossibly lucky.

Obama's thumping re-election may never silence the ravings of the extremists. But Tuesday's election victory should at least set to rest the notion - sometimes held by his own supporters - that Obama could not fill the office of the presidency. He was no Bill Clinton, no Ronald Reagan, no FDR. Right?

Wrong. President Obama's first term was a frenzy of big legislation: the massive stimulus spending of the Recovery Act, equal pay laws, healthcare reform, Wall Street reform, the repeal of Don't Ask Don't Tell, a nuclear treaty with Russia. If anything, voters said in 2010 that Obama's agenda represented too much change; they wanted him to slow down and work with Republicans.

That is the message voters have once again sent to their elected officials in Washington: work with each other. After all, the American system was set up to do just that. By sharing power between the president and congress, the founding fathers wanted to make it hard for any single leader - like a monarch or prime minister - to exercise power unilaterally.

Fortunately, that won't be hard for Obama. As he showed in the final days of his campaign, he is happy to work with any Republican, no matter how harsh a critic, to get stuff done. That's what was striking to so many voters as they watched him embrace the New Jersey governor Chris Christie in the aftermath of Hurricane Sandy.

The pugnacious governor was hardly shy about taking a baseball bat to Obama's politics and record. Yet he was as effusive about Obama's leadership after the storm as the president was determined to help Christie to succeed.

At this point, conservatives tend to scoff at this clearly delusional analysis of Obama's character and politics. After all, he passed healthcare reform with no Republican support. He favours regulation of their friends in big business. And he has said mean things about Republicans in Congress.

So, for the scoffers, it's time for a reality check. Republican leaders met on the night of Obama's inauguration to plot their path back to power. At the heart of the strategy was a disciplined and determined approach to obstructionism: deny Obama any legislative victories, and any claim to bipartisanship, in a permanent campaign to claim back some part of Washington.

That strategy worked in the House of Representatives, with its narrowly gerrymandered districts. It has failed twice in the Senate, and now also with the presidency. Republicans cannot obstruct their way back to power in any meaningful way.

What does this mean for Obama's second term?

First, the President is both ambitious and pragmatic. He will shoot for some big legislative victories, at the same time as seeking Republican partners. Progressives may be dismayed by his readiness - even in a second term - to reach out across the partisan aisle. But that is the essence of a politician who promised on Tuesday night, as he has since he first burst on to the national stage in 2004, to unite red and blue America.

Second, Republicans need to wake up and smell the coffee. Exit polls showed clearly that the litmus tests of their primary campaigns - on abortion, immigration and taxes - are not the majority positions of Americans. A clear majority - 59 per cent - of voters support abortion in most or all cases. Almost two-thirds support the idea of giving illegal immigrants a path to legal status. And 60 per cent support raising taxes on all Americans or those earning more than $250,000 a year.

If Republicans want to restore themselves to power, they need to start embracing those positions now. Because, in all likelihood, the economy will not be struggling to recover in the mid-term elections of 2014 or the presidential elections of 2016. Unemployment will be too low to argue that the Democrats have failed; an argument that was insufficient for Romney to win the presidency this week.

In the short term, Republicans in Congress will work with Barack Obama to deal with three big tax-and-spend challenges before the end of the year. The so-called fiscal cliff involves the need to raise the national debt ceiling, the end of the Bush tax cuts, and deep cuts to defence spending that were triggered by the failure of the last round of budget talks.

In two of those three rounds, Obama holds the trump card. Republicans sorely want to extend most of the tax cuts and avoid defence cuts. The president clearly wants to avoid another reckless flirtation with defaulting on US debt, and he wants to raise taxes on the wealthy to help close the federal deficit. You don't need to be a rocket scientist to see where the compromise lies, or when it will be reached: before the new Congress takes power in January.

Beyond that, immigration reform is perhaps the biggest domestic priority that Republicans will need to embrace. If the party continues with its current plunge among Latino voters, then it will lose its hold on Texas - the biggest reliably Republican state - in as little as a decade.

Soon Obama will revert to the corner where all second-term presidents eventually find themselves: foreign policy. As their domestic power fades, presidents discover no end of crises where the leader of the free world can make a real difference.

There is no shortage of work for Obama beyond America's shores. He will wind down the war in Afghanistan in two years. He will continue to squeeze Iran's economy and leaders, and possibly take more concrete action to stop its nuclear ambitions. And he will surely be tempted to bring the Israelis and Palestinians back to the negotiating table.

By then, he will be the subject of a new term of derision. Some will want to use it now, or early next year. But President Obama has at least a year, and maybe two, before he truly deserves to be called a lame duck.

Richard Wolffe is the Executive Editor of msnbc.com and author of the Obama books 'Renegade' and 'Revival' - The Independent