The second most powerful person in the western hemisphere arrived in Washington on Monday. But the most powerful one spent most of the day rolling Easter eggs on the South Lawn.

Dilma Rousseff, the Brazilian president, leads an economy larger than Britain's, commands an ocean's worth of oil, and enjoys a 77% approval rating her American counterpart can only fantasise about. Everybody but Barack Obama wanted to see her this week. She arrived to the accompaniment of a half-dozen op-eds from professors and thinktank bosses, all of them extolling her economic stewardship and begging DC to take her seriously. The presidents of Harvard and MIT (both women, for what it's worth) invited her up to Boston. Even the US chamber of commerce put out the bunting – surely the first time the big bad business group has been so excited to meet a former Marxist guerrilla. Only Obama shrugged.

The two presidents had a short meeting and a shorter press bilateral, during which they never looked each other in the eye. About the only boost to bilateral ties that came out of their confab was a deal to promote the importation of cachaça – wonderful news for caipirinha drinkers, sure, but not exactly an agreement of world-historical importance. Not only did the US president not bother with the trappings of a state visit; he barely gave Dilma two hours. "Obama could have taken her to dinner," one Brazilian official groused. "Or to the Kennedy Center."

The leaders of India and China get pomp and circumstance when they come to town. Vladimir Putin is a big enough operator that Sarah Palin blessedly keeps watch on his nation from her house. But Brazil is the Brics country that gets no respect, even in 2012. We still speak of it as a basket case, which would be patronising even if our own country weren't in the grips of a rejectionist Congress and a politically motivated supreme court. Yet of all the big emerging economies – a ridiculous phrase now that they have already emerged, while our own and Europe's seem to be receding into nothingness – Brazil is the one that poses the least significant geopolitical threat and offers the most advantages, as all those salivating CEOs already know.

So why did Obama, who has already demonstrated his prowess as a salsa dancer, decline to put a little samba in his step as well? It's tempting to imagine that, in an election year, the White House was reluctant to spotlight a much more successful economy than our own, where massive growth and reduced inequality go hand in hand. But I'm afraid the real reason is simpler: with respect to the boardroom optimists advocating some grand inter-American compact, this is just how Washington does business. In history class, the first lesson students learn about American foreign policy is the Monroe Doctrine – the 200-year-old principle that Latin America is our turf. We do what we like and tell everyone else to keep out. The idea that a Latin American country could actually serve as a model is beyond our comprehension. Now, for the first time, a second major power is rising on the block, but among us gringos the old big-stick habits die hard.

More and more, alas, the US looks like it is conducting a Norma Desmond foreign policy: hallucinating that it hasn't aged and withered, unable to accept that the world is changing and that its powers are in decline. Voters seem to know full well that the days of uncontested American supremacy have come and gone, which makes it all the more pitiful that our government still can't accept the altered state of things.

That stood out particularly this week, and on the substance of Dilma's visit as much as the optics. One goal that almost everyone agrees on is an end to requiring visas for visiting Brazilians – though on the evidence of the throngs of lusophones I saw descend on a Miami shopping mall last month, that's not enough to keep them away. (Brazilians spend the most tourist dollars per capita in the US, splashing out $5,000 a visitor.) Yet the White House announced on Monday that the visa rules are staying in place, and tried to celebrate that it takes "only" 35 days to get a sticker in your passport from the São Paulo consulate.

A bill has been proposed to relax the rules. It is stuck in the Senate. The fear, naturally, is illegal immigration. Which shows just how behind the times the US remains: as if any Brazilian these days would come to America for a job.

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