For the prime minister and representatives of Team Dave trying to stay cool in the Washington heat, the carefully manicured narrative they have been in town to polish is all about the deep, warm, "special" relationship between the Brits and the Yanks that stretches back generations.
It is a story built upon common respect and mutual trust founded on shared adversity. Having stood shoulder to shoulder during days when bullets have flown and blood has flowed, the US and UK enjoy a profound friendship that can withstand the occasional squabble over spilled milk or oil. So the conventional narrative goes.
To political strategists, the conventional narrative is what matters. It can bear little relation to truth but contains a magic ingredient - authenticity.
I am on holiday with my family in Florida but cannot stop myself puzzling over this "special" bond. Flicking through the hundreds of TV channels, I have bumped into a number of portrayals of the British.
There was a dumpy woman in a hat and two-piece suit endorsing a local car dealership who, it emerged, was supposed to be the Queen. A comedy show had two "frightfully-awfully" Englishmen playing croquet. A kids' programme featured a familiar British detective with deer-stalker and pipe apparently suffering from a comic overdose of etiquette.
They are quickly drawn caricatures which play to a popular narrative in which the English have blue blood while the Americans have red necks. (The Scots, Irish and Welsh are exotic in different ways.)
The screen-writers like to contrast the intense breeding and polished manners of their cousins from across the pond with the classless informality and artless sincerity of the locals. It celebrates US authenticity.
However, within the narrative there is also a sub-plot: that unpretentiousness might be mistaken for unsophistication; an anxiety that, even today, Americans might be seen by Europeans as arrivistes lacking cultural patina.
There is a concern that authenticity might be measured in centuries of natural weathering rather than the repro distress routinely applied to new blue jeans on the rack at Banana Republic. It is a contradiction that sits at the core of the relationship between the UK and the US.
When President Obama told David Cameron yesterday that British-American bonds were "truly special", he was saying the words that fitted neatly into a useful media story.
There are good reasons for both men to want to promote shared values and visions as their troops continue to fight and die together on distant battle-fields. But the special relationship is much more than a reflection of political expediency, as I discovered in the Three Broomsticks pub in Hogsmeade.
"I like to think we are bringing the British sensibility to life", my drinking companion told me. "It is about being authentic - being true to the fiction".
Mark Woodbury is the creative magician behind the Wizarding World of Harry Potter at the Universal Studios theme park in Orlando, an alchemist who searches for ways of manufacturing authenticity from fibre-glass and fireworks. "There are three essential ingredients" he revealed, "and JK Rowling provided all three."
The queue for the park's latest and very British attraction has stretched through the resort and out the front gates, such has been the power of the spell cast by the Harry Potter phenomenon.
People are wondering out loud if this can change the balance of power between the mighty Disney and its Universal rivals. So what are the three ingredients of theme park authenticity potion?
"Firstly, likeable characters that are not nostalgic, that are about today", Mr Woodbury confided over a Butterbeer. "It must also be about taking people to places they couldn't otherwise go to and there must be a great sense of adventure and action."
He explained how he had read the books to his younger daughter and realised after the first couple that "this was a theme park waiting to happen".
"But what makes this place authentic?" I asked. "We make it real" he replied, telling me how many guests are so overcome by the experience that they burst into tears as they step into the world.
JK Rowling's narrative speaks to people as powerfully as any of the political stories we read in the papers each day. The world of battling wizards and witches is no less "true" than the warring factions inside the Westminster or Washington bubbles.
It is a child of the special relationship: a British writer along with an Oscar-winning British set-designer in Stuart Craig have collaborated with some of the finest technical and creative talents in the United States to bring a very British literary series to life on the Florida swamp.
It would be easy to scoff, but Harry Potter is a multi-billion dollar global phenomenon that has inspired a world-wide fan-base structured around the traditions and manners of the English public school system.
The souvenir shops are selling uniforms, scarves and house robes to customers so desperate to purchase a slice of genuine Hogwarts that they queue for hours for the privilege of being allowed to enter the overcrowded store.
In the Harry Potter books there is a potion called Veritaserum which forces those who have drunk it to tell the truth. It takes a full moon-cycle to mature. But making truth from fiction requires a longer gestation.
"These are really, really difficult things to do" Mark Woodbury admitted. "We had a great collaboration over five years that helped us along every step of the way to ensure we made it the most authentic possible".
Manufacturing authenticity from fantasy - now that's a magic trick that the teams in the White House and Downing Street wish they could pull off every day.