Kurt Volker, George W. Bush’s final NATO ambassador and Mr Obama’s first, suggests that—despite Mr Obama’s distrust of military force—he would still act if there were a loud enough “domestic outcry”. An outright invasion of a NATO ally would trigger such an outcry, Mr Volker says, as would a serious attack on Israel. But short of that, Mr Volker worries that other countries see within Team Obama “a creeping willingness to let things go”.

A senior former defence official says that Mr Obama acted slowly in sending reinforcements to NATO members, and would do so again. “I think Mr Putin is going to keep coming until someone stands up to him,” says this source. In the case of Russian adventurism inside NATO’s borders, he predicts that Team Obama would respond: “I would worry that it would be late. Not too late, but late, and that would send a message around the world.”

America’s obligations in Asia are “nuanced”, says another senior figure. Where American troops are stationed in large numbers—in South Korea, or on the main islands of Japan—the security commitment is “absolute”. Under Mr Obama, American forces have pushed back (somewhat) against Chinese sabre-rattling in disputed seas. Should China threaten Taiwan, America would feel a “moral obligation” to send ships or planes to serve as a referee. Yet during previous crises, as in 1996, when China tested missiles before a Taiwanese election and America sent warships to the area, even hawkishly pro-Taiwan members of Congress privately told officials “you’d sure as hell better not get us into a war with the Chinese”, this source recalls.

A skirmish over the Senkakus would trigger help of some sort, says another veteran of many crises: perhaps early-warning planes to patrol the skies for Japan, and warships to show the American flag. But the American public “would not be excited to go to war over a bunch of rocks”.