Even more extraordinary is the founding father's entourage. The notion that Islamic martyrs happily go to their deaths in the expectation of 72 virgins to comfort them is one of the great western clichés of modern times. Yet here in the Capitol we see the elderly Washington floating up in the midst of 13 virgins, one for each of the original American states.
Does this just prove that masculine fantasies are the same in every society, or is it a warning not to criticise another culture before examining one's own? Either way, the fresco is an intriguing image in a week when both the House and Senate resolved to end the US's disastrous crusade in a Muslim country.
Four years after the Iraq invasion, a sea change has come over this country. Until you spend a few days here, it is hard to take on board how massive it is. Congress, for the first time, has set a timetable for pulling out of Iraq. After constant warnings from the White House that this will "delight the terrorists", the House and Senate called Bush's bluff.
In itself their change of heart is not bold, since polls have shown for months that most Americans want to end the US role in Iraq. Last November's elections sharpened the message. The remarkable thing is that Congress, and in particular the Democratic party, has listened so quickly.
In the first weeks after November the party hesitated for fear of being blamed for lack of patriotism. Now the Democrats' line echoes the bumper stickers: "Support our troops, bring them home."
In the House the debate was at times agonising. Radical Democrats felt the deadline proposed by the party leadership for the last combat troops to leave Iraq by the end of August next year was too far into the future. They also worried that the resolution implicitly backed the current "surge" of extra troops to Baghdad. From the press gallery their frustration was palpable. Yet one by one several potential rebels lined up at the microphones to say they would support the late date rather than let the Republicans defeat the measure.
The Senate's resolution is tougher. One clause shortens the deadline to the end of March next year. Although this is non-binding, another clause mandates the president to start the draw-down within the next 120 days.
Bush says he will veto the measures. Yet this matters less than the fact that Iraq has run far into the lead as the number one issue for next year's presidential contest, and the war party is on the defensive. Among the Democratic contenders Hillary Clinton remains the most cautious. Last week she and Bill walked down a catwalk holding hands above several hundred fans in her first campaign fundraiser in Washington. Each had paid at least $1,000 for the half-hour cameo, but Clinton devoted only two sentences of her speech to the war, vaguely pledging that "if this president doesn't extricate us from Iraq before he leaves office, I will".
Signs of collapse in public support for the war are everywhere. On a foray to the south, one of the most conservative regions and the site of numerous military bases, I found the anti-war mood surprisingly strong. In Alabama I heard a young officer, still serving in the navy, tell a meeting organised by "Veterans for Peace" that he had stood that morning outside Maxwell airforce base in the state's capital, Montgomery, holding an anti-war poster. Scores of people driving in gave the thumbs up or honked their horns, he said with pride.
At Auburn University a quarter of the students in a class I visited had close relatives in Iraq. Home on leave, they all say they hate it and think the war is pointless.
In short the US debate on Iraq has leapfrogged beyond Britain's in a way that Labour seems not yet to have taken on board. Tony Blair destroyed himself with his disastrous decision to join what Senator Jim Webb, one of the best US Democrats, calls Bush's "careless aggression". But when will Labour as a party change course?
The US system is different, and Congress can oppose the executive in a way that a British parliamentary party rarely does when its leader is prime minister. But the leader himself can adjust. The Brownites say their man is wondering how to differentiate his Iraq line from Blair's. The best way would be to name a clear date for Britain's troops to come home, as the Democrats have just done. Follow the US lead, this time for peace, not war.
More than that, every Democratic presidential contender who supported the war - apart from Clinton - has apologised now. Where are Labour's regrets? Why are Labour ministers, and the chancellor in particular, not held to account in the same way? When the current mini-crisis over the British sailors held in Iran is over, Labour should stop the post-imperial posturing. Let it admit its forces should never have been in or near Basra in the first place. And let's hear a clear apology to the British people for the entire war.
