“If anybody in this room thinks Putin will stop at Ukraine, I assure you, he will not,” President Biden said during his State of the Union address on Thursday night. Europe is “at risk,” he added, as he welcomed Ulf Kristersson, the prime minister of Sweden, the newest member of NATO.

But Mr. Biden also said he remains “determined” that American soldiers will not be necessary to defend Europe. As a White House spokesman put it last week, it is “crystal clear” that the use of ground troops is off the table.

Mr. Kristersson’s head must have been spinning. The prospect of further Russian incursions was the strongest argument that the United States relied on to draw NATO into the war, and to draw new members, like Sweden, into NATO. But if such incursions were a genuine concern, then ground troops would be an option for the United States and its allies almost by definition.

The rationale for NATO participation in the Russo-Ukrainian war is getting fuzzier at the very moment when one would expect it to be getting clearer.

This is a problem. Europeans, like Americans, are tiring of the war. They are increasingly skeptical that Ukraine can win it. But perhaps most important, they distrust the United States, which has done little in this war to dispel skepticism about its motives and its competence that arose during the Iraq war two decades ago. Unique though Americans sometimes believe their polarization to be, all Western societies have a version of it. As Europe’s “elites” see it, NATO is fighting a war to beat back a Russian invasion. But as “populists” see it, American elites are leading a war to beat back a challenge to their own hegemony — no matter what the collateral damage.

American leadership is failing: That is the argument of an eccentric new book that since January has stood near the top of France’s best-seller lists. It is called “La Défaite de l’Occident” (“The Defeat of the West”). Its author, Emmanuel Todd, is a celebrated historian and anthropologist who in 1976, in a book called “The Final Fall,” used infant-mortality statistics to predict that the Soviet Union was headed for collapse.