THE American president touched down in London last night for a three-day visit. Officially his trip has to do with wishing the queen a happy 90th birthday. In practice it is a carefully worded bid to nudge British voters towards a Remain vote in the EU referendum on June 23rd. His lobbying began this morning with a column in the Daily Telegraph (seemingly chosen for being the most high-brow Eurosceptic outlet) under the headline: “As your friend, let me say that the EU makes Britain even greater.” This afternoon he will give a press conference in Downing Street where he is expected to reiterate these arguments. The Leave camp is furious at the intervention, calling it a diplomatic impropriety. Boris Johnson has a counter-column in the Sun today urging the president to butt out and, rather oddly, insinuating that as a “half-Kenyan” his views reflect resentment of Britain’s colonial past. In truth this is sour grapes. For many on the Leave side quitting the EU is a first step to building a new Anglophone alliance, led by Britain and America and extending across the Commonwealth. How ungrateful, how unAmerican, how un-Anglo-Saxon of the president to reject this thrilling fantasy. But most of all they are angry because his comments will hurt their cause. America’s president is popular in Britain. Brexiteers know that voters will take his arguments seriously: the most resonant yet of the line-up of credible, authoritative voices—the Bank of England, the IMF, business leaders, former prime ministers—whose warnings form a steady drum-beat that should stay Brexit-inclined voters’ hands on referendum day.

Mr Obama’s comments stand out among these not just for their weight, but for their optimism. “You should be proud that the EU has helped spread British values and practices”, he noted in his column: “The European Union doesn’t moderate British influence—it magnifies it.” Other interventions have focused more on the disadvantages of Brexit: the risk to growth and jobs, questions unanswered by the Leave camp, the dangers of a fragmenting Western alliance in uncertain times. And that is right. Britons are not natural pro-Europeans. There is no latent zeal for European unity lurking, ready to be unleashed, just under the surface of British society. Nervous urging from keen Europhiles that the Remain campaign show more “passion” about the joys of European integration are, I’m afraid, too optimistic about the public’s appetite for such entreaties. “Britain Stronger in Europe” has conducted the focus groups, commissioned the polling and tested out its messages and on that informed basis is concentrating on the risks of Brexit and the transactional benefits of membership—a case, in other words, that rings true to a sceptical audience.

Yet there is nonetheless a place in the pro-European toolbox for the sort of arguments put forth by Mr Obama. For too long the Leave crowd have got away with painting the pro-Europeans as the gloom-mongers, the people who think Britain so small and insignificant that it needs to hug tight to its sclerotic neighbours. In this vision, the bold and ambitious national strategy is to break loose and reemerge on the world stage. “Britannia can rule the waves again!” as one Brexiteer put it at a debate I recently attended.

The retort, which the Remain camp could perhaps make more often, is the one put by the president. Britain has long pushed the EU in a liberal, outward-looking direction. Think of the Lisbon Agenda to make the EU more competitive in the last decade, the eastwards expansion (one of the most significant triumphs of British foreign policy in decades), the Iran nuclear deal, the moves towards TTIP today. As president, Mr Obama has broadly neglected the transatlantic relationship, but tellingly even he has been moved to urge Britain not to perform such a self-mutilating move (damaging to his country too insofar as a dynamic and effective Europe is in American interests) as to throw all this away.

And all that is without Britain much bothering to use the EU to project its interests. Compared with its neighbours, it does little to push its brightest administrators and politicians into the European institutions. Until recently Mr Cameron had few real Europe experts in Downing Street (compare that to the German chancellory, which has almost an entire wing devoted to Europe policy). Apart from a handful of Europhile and Europhobe die-hards, few MPs are much interested in the EU; attendance at the European Scrutiny Committee in Parliament in the 2014-15 parliamentary session was just 48.7%. Some of David Cameron’s European policies—pulling out of the European People’s Party, his botched veto in 2011, threats to endorse a Brexit vote last year—have hardly helped the country promote its agenda in Brussels.

Given how much Britain manages to influence the EU despite all this, what it could achieve if it actually tried? If it resolved, over ten or fifteen years, to remake the union in the British image? That ambition is less far-fetched than it might look. New geopolitical and security threats play into Britain’s long-standing desire to make the EU more outward-looking and security-conscious. The urgent need to make Europe more competitive—an agenda now being championed even by the French and Italian governments—similarly responds to traditional British priorities. For all the talk of integrating the euro zone, fellow northern European member states will want to ensure they are not simply yoked to poorer, more sluggish southern economies. Other non-Euro-zone states will be wary of caucusing and want to ensure that the EU continues to operate at 28 rather than 19. These developments create political opportunities for Britain.

Indeed, euro zone or no euro zone, no EU state has an automatic claim to leadership. France is a big military power but has a struggling economy. Germany is an industrial powerhouse but reluctant to lead on defence matters. Neither has a global financial centre to rival London. In a Europe of overlapping and concentric circles, perhaps Britain, an unsentimental member state with one foot in Europe's centre, one in its periphery and an eye on the wider world, is best-placed to lead.

The demographic and economic shifts of the coming years also bear consideration. By 2030, according to some estimates, Britain will be the largest economy in the union. It is also on track to overtake Germany and become its largest member state. That in itself should pay dividends—numerical, in the Parliament and institutions—and symbolic.

For the reasons explained above, I am not convinced that all this should be the backbone of the Remain case, useful though Mr Obama's intervention today is. But it does give the pro-Europeans something with which to parry Eurosceptic defeatism ("Britain has virtually no influence in Brussels" bellowed a recent Express headline) and accusations of talking down Britain's prospects and ambitions. Perhaps the moment at which to make this argument in full will be after a Remain vote (if indeed that is the referendum's outcome). If his gamble pays off Mr Cameron will have a window in which to reframe his country's place in Europe and describe a new course, before eyes turn to the next big political drama: the battle to replace him. A path forwards to sceptical, pragmatic British leadership in a continent that badly needs it would be a legacy indeed. As Mr Obama might put it: "Yes we can!"