For some British and American conservatives, a special relationship litmus test has been the location of Winston Churchill's bust in the White House--witness the fretting when President Obama moved it out of the Oval Office. But the activity in think-tank land east and south of Washington's Dupont Circle now tell their own
story.

The Atlantic Council has held more than a half dozen Brexit sessions, highlighted by the appearance of three former National Security Advisors to voice their concerns. The Brookings Institution put on a three-panel session that included a debate and economic analysis. Pessimistic economic forecasting was front and center at the Peterson Institute for International Economics. A pro-Remain Member of Parliament Tobias Ellwood did double Washington duty--the morning at the Atlantic Council and the afternoon at the Center for Strategic and International Studies. He sidestepped a question of whether his Tory Bournemouth constituency would vote for Remain or Leave, and the CSIS moderator suggested he try a more positive line of argument.

And a week before the referendum, the oldest of the think tanks, the Council on Foreign Relations, offered a morning of unabated pessimism on politics in the United Kingdom, Britain's relationship with Europe and in the world beyond. Even an audience question about the consequences of a remain vote yielded a gloomy response from panelist Sebastian Mallaby of deeper political polarization and turmoil in Britain, especially in the ruling Conservative Party.

The dire prognoses of a leave vote ranged from the strategic, whether a Britain outside the EU would spend and care to defend Europe in NATO, to the prosaic, that Brexit would strand two million British pensioners in Spain and elsewhere without national health insurance.

The Council session brought forward a deeper worry that the Brexit referendum is not only about Britain and Europe. It could have implications for the United States. As Financial Times U.S. columnist Edward Luce recently wrote, that anguish is summed up in two words--Donald Trump. This linkage was first pushed by Republican pollster Frank Luntz in a Time.com commentary. He described the Brexit vote as "a canary in the coal mine" for an anti-immigrant, anti-elite populism that could give fresh wind to Trump's election prospects in the United States.

"Brexit legitimizes the populist movement," said Council panelist Adam Posen, president of the Peterson Institute and a former external board member of the Bank of England's Monetary Policy Committee. Indeed, Trump, the presumptive Republican nominee for president, is the only major American politician to voice support for Brexit. And perhaps not coincidentally, he will be in Britain the day after the referendum at one of his golf courses and surely in the spotlight.

While Trump's Brexit remarks were brief and off-hand, President Obama made a full-tilt pitch for Remain at a joint London news conference with Prime Minister David Cameron, a highly unusual intervention in another country's politics.

While asserting that the special relationship would continue, "hopefully, eternally" regardless of the vote, he added: "The U.K. is at its best when it's helping to lead a strong European Union. It leverages U.K. power to be part of the EU. I don't think the EU moderates British influence in the world, it magnifies it." Polls subsequent to Mr. Obama's intervention have shown growing support for Brexit.

At the Council and elsewhere, words such as "terrified" and "nightmare" lace the conversations, accompanied by the awareness that no one here other than expatriate Britons with absentee ballots can directly affect the outcome and its impact on the special relationship.That frustration and its reality was summed up by an august figure in think tank land, Brookings president and former Deputy Secretary of State Strobe Talbott. As he wrote recently: "Mr. Cameron, as remainder-in-chief, wants to preserve Winston Churchill's vision for Europe and the special relationship with the United States. The question is: Do Britons?"