Not to put too fine a point on it, past meetings of the leaders of the West's major economic powers have all too often been a waste of time. But the G8 gathering that opened yesterday at the presidential retreat of Camp David, and then segues into Sunday and Monday's Nato summit in Chicago, is an exception. Indeed, it may be the most important since the very first of its kind took place at Rambouillet in 1975.

The Camp David talks will be dominated by the euro crisis, while Nato will focus on speeding an exit from the 11-year-old war in Afghanistan. In Chicago, demonstrations are likely, ostensibly against the war, but in reality driven by motives akin to those behind the protests in the streets and at the ballot box in European countries buffeted by the euro storm. There is a pervasive sense that, everywhere, politicians are failing the people. The US-led system whose uncurbed excesses produced the past four years of financial turmoil and economic misery is also the one that has been unable to extricate itself from the ever-more unpopular Afghan conflict even as it watches impotently as a tyrant in Syria wages war on his own people.

Of these challenges for the West, the most pressing is the euro, whose demise in its present configuration may be only months, if not weeks, away, if nothing is done. If Greece withdraws, as may yet happen, it would be proof that euro membership is not eternal, and pressure would switch to the far larger economies of Spain and Italy.

At that point, Europe would be staring at the collapse of its most ambitious project, with consequences, economic and political, immediate and longer term, that are impossible to foresee. And in an interconnected global economy, everyone would be affected. The US is at risk, despite its banks and corporations reducing their exposure to the eurozone, and the advantage stemming from the dollar's role as the main reserve currency. Calamity in Europe might well send the stuttering US economy back into recession. And for President Obama, the timing could not be worse as he fights to win a second term in what is already likely to be a close election in November.

No one expects these four days of summitry to serve as a magic wand. Great problems are not solved by communiqués. What is to be expected, however, is a determination to deal with the crisis, and a broad consensus on how. The central drama is playing out in Europe, but, as host of the meetings and leader of the world's largest economy, a special responsibility falls on Mr Obama's shoulders.

First and foremost, he must argue that the issue is not a black-and-white choice, between "one-size-fits-all" austerity and pumping vast amounts of cheap money into already highly indebted economies.

In each country, the solution will be different. Germany, for instance, must boost consumer spending and imports, even – horror of horrors – at the price of higher inflation. Meanwhile, the profligate southern Europeans have to cut back their bloated and unaffordable public sectors, while simultaneously taking measures to boost growth.

The problem lies in buying time to square this circle. Europe's tangled history has thus far ruled out the political union that should have underpinned its leap to a currency union. If the euro is to be saved, there will have to be an ad-hoc union, most likely in the shape of new "euro bonds" guaranteed by all, including Germany.

We can but hope that the wooded tranquillity of Camp David concentrates minds on the problems at hand. The world, and history, will not wait.