Yet polls find that Americans do not want Mr. Obama to get the country enmeshed more deeply in places like Ukraine and Iraq, suggesting that he is more in touch with a broader public desire for disengagement than many of his critics even though his leadership is in question.

“Just because there are lots of global challenges doesn’t mean you have to overreact on one just to make a point,” said Benjamin J. Rhodes, his deputy national security adviser. “They each have to be managed carefully in their own right. We have longer run plays that we’re running. Part of this is keeping your eye on the long game even as you go through tumultuous periods.”

Others said that long game was sometimes hard to detect in what seemed an ad hoc foreign policy. “If they had a strategy that allowed allies to understand what we’re likely to do — the principles guiding our choices — they could take coordinated and strengthening actions,” said Kori Schake, a former aide to President George W. Bush now at the Hoover Institution. “But their unpredictability discourages others from acting, which is where ‘leading from behind’ runs aground.”

The confluence of crises seems to confront Mr. Obama almost with each passing day. He has been pressing Chancellor Angela Merkel of Germany to force a more robust European response to Russian aggression just as the relationship ruptured again over a new report of American spying in her country.

Hoping to smooth things over, Mr. Obama dispatched his White House chief of staff, Denis R. McDonough, and counterterrorism adviser, Lisa Monaco, to Berlin, where they met with German officials on Tuesday, even as European foreign ministers were meeting separately to consider new sanctions on Russia.