European leaders have just spent another summer weekend working on the elusive task of finding a way out of the Greek financial crisis. It is a story of ever receding deadlines and intense European politics, pitting Greek public opinion against German financial rectitude.

The proximate issue is whether Greece can remain part of the Eurozone, the congeries of European Union (EU) member states that have abandoned their national currencies in favor of a common currency, the euro. Lurking in the background is the deeper issue of whether Greece can continue as an effective member of the EU. There is no precedent for a member leaving the EU. Such a prospect is fraught with uncertainty and, in Greece’s case, danger.

As Greek public opinion has weighed in ever more loudly, the country has taken a political turn and entrusted the task of negotiating an outcome to an untested and impetuous Prime Minister, Andreas Tsipras. His tactic has been defiant and unconventional. He has sought out Russian President Vladimir Putin, who has been only too willing to grab the opportunity, at no cost, to annoy the West. And now Tsipras has topped off his negotiating strategy with a call for a referendum on the package of financial measures to be agreed with Greece’s creditors. Meanwhile, the Greek government has halted capital transfers and shut the banks.

Faced with mounting Greek intransigence, the mood of European leaders has evolved from exasperation to disgust. After tedious and fruitless negotiations to keep Greece within the Eurozone, they seem to be coming to the conclusion that the time has come to cast Greece off.

If this were to happen, Greece would no longer be a member of the Eurozone and presumably reintroduce the drachma. It would still be a member of the EU, though its standing would be severely compromised. Athens would no longer be able to count on Brussels’ good will and largesse. To some, Greece might acquire the sobriquet of failed state, with the wrenching challenge of hoisting itself financially by its own petard. President Putin would see an opportunity for mischief.

Such a turn of events would serve neither European nor American interests. In 1947, President Truman declared the American interest in a democratic, secure and prosperous Greece. This interest continues to this day. The principal responsibility for working out an arrangement that keeps Greece within the EU fold lies with the EU. But Washington is not without means to play a helpful role in encouraging an outcome that avoids a “Grexit.”

Marten van Heuven is a lifetime board member of the Atlantic Council.