The risk of Britain voting to leave the European Union in a June referendum has been rising steadily since the start of the year, unsettling business and markets from Asia to America.
With commodity prices still low and growth weak, finance ministers from the Group of 20 leading economies noted in a communique earlier this year, "the shock of a potential U.K. exit from the European Union" would add to the woes facing the global economy.
Now, half way through the referendum campaign, the most powerful leader of the free world has entered the domestic U.K. debate over Europe. The consequences could be decisive.
Opinion polls were suggesting that with two months until the vote, the "Remain" camp held only a slender lead, with the "Leave" side gaining ground and a significant bloc of voters still undecided.
Remain's cheerleaders, Prime Minister David Cameron and his finance minister George Osborne, were struggling. Cameron was fending off unwelcome questions about his family finances after disclosures in the Panama Papers that he had benefited from an offshore fund set up by his father; Osborne was attempting to recover from political misjudgements in his annual budget.
Financial markets were jittery. The pound has slumped up to 7% this year against the dollar and up to 10% against the euro on Brexit nerves. Some foreign-owned companies, such as French power utility EDF, have deferred big U.K. investment decisions until after the vote.
Then came Obama's broadside. The U.S. President used a visit to the United Kingdom last week to deliver a strong message on Europe which may mark a turning point in the referendum campaign.
To the fury of the "Brexiteers", as those arguing to leave the EU are known, Obama declared that if Britain left, it could forget about securing a quick new bilateral trade pact with Washington -- a key assumption made by the Leave campaign.
The U.K. would instead go to "the back of the queue" for a trade deal, behind other larger blocs such as the EU, the U.S. leader added, using unexpectedly blunt language. Obama even quoted from the famous English poet John Donne, saying "no man is an island" and pointing out that influential nations in the 21st century did not "go it alone".
The U.S. was best served by a strong Britain inside Europe, he concluded.
The Leave campaign responded with ill-tempered jibes about lame-duck presidents, accusing Obama of hypocrisy for suggesting that the U.K. swallow a surrender of sovereignty which he would never propose at home. "Obama is asking the British people to accept a situation that he patently would not recommend to the American people," tweeted Vote Leave.
But in a potentially fatal blunder, leading Brexiteer and London mayor Boris Johnson accused Obama of removing a bust of British wartime leader Sir Winston Churchill from the White House because of a grudge motivated by "the part-Kenyan president's ancestral dislike of the British empire."
Johnson's crude remarks prompted a storm of protest, with Churchill's grandson, Tory MP Nicholas Soames, describing them as "idiotic." "Boris Johnson has really bogged it and showed himself up as an ocean-going clot," he tweeted.
Obama pointedly noted at a news conference that he still had Churchill's bust on display in the White House because "I love the guy" and the mayor was forced onto the defensive.
Overnight, the charismatic Johnson turned from one of the Leave campaign's strongest assets into a liability, accused of making a serious political misjudgment and, at worst, of indulging in crude racism.
Fresh opinion polls have not been published since Obama's high-profile intervention but pollsters expect his comments to give a noticeable boost to the Remain camp.
"Obama's intervention was pretty important because he is hugely popular in Britain," said Hugo Dixon, who runs the InFacts website, which makes a fact-based case for the U.K. to stay in the EU. "Most importantly, he is very popular among the undecided voters. And he was not ambiguous at all. He was very clear that Britain's influence is magnified, not diminished by the EU."
Obama's comments came at the end of what commentators are describing as the Remain campaign's best week.
Chancellor of the Exchequer Osborne had released just before Obama's visit a detailed Treasury study of the costs of Brexit. In 206 pages of densely-worded analysis, the mandarins concluded that leaving the EU would cost every family 4,300 pounds ($6195) a year in lost economic output. Foreign direct investment would plunge 20% by 2030.
These estimates were based on the assumption that Britain would secure a negotiated bilateral trade agreement with the EU similar to the ones enjoyed by Turkey, Canada or Switzerland. Were that not possible, the costs would be higher still, officials said.
Brexiteers poured scorn on the Treasury's "scaremongering" but the exchanges highlighted one of the Leave campaign's biggest problems: its failure to offer a coherent vision of what the U.K.'s future would look like outside the EU.
Leave officials have avoided committing themselves to any particular type of trade agreement with other countries, saying only that they are confident that good market access could be secured.
Their case was not helped by the head of the U.K. Statistics Authority, Sir Andrew Dilnot, describing the Leave estimate that the U.K. paid 350 million pounds a week to Brussels for membership as "potentially misleading" because it did not include rebates and EU grants back to the U.K.
Obama's remarks, plus the Treasury's numbers broadside and the questioning of Vote Leave's figures and tactics, have given the Remain camp a much-needed shot in the arm.
It is not yet clear, however, whether the help from Washington will be enough to persuade Britons, who are notoriously unenthusiastic about Europe, to turn out in force and cast their votes to stay in Europe.
If the official estimates of the cost of life outside the European Union, and Obama's predictions of the difficulty of securing trade agreements if Britain goes it alone turn out to be correct, staying at home or voting to leave could prove costly for citizens of the United Kingdom on June 23.
Michael Stott was UK News Editor at the Financial Times. He is now on assignment from the FT to the Nikkei Asian Review.