UNITED NATIONS — If one snapshot from his swing through Washington and New York this week captured the position in which Prime Minister Benjamin Netanyahu of Israel finds himself, it wasn’t when he sat beside President Trump on Monday and saluted him as a modern-day Cyrus, Balfour and Truman rolled into one.

Or on Tuesday when Mr. Netanyahu reveled in the adulation of 15,000 cheering American Jews as he reeled off a TED Talk-style sales pitch about Israeli economic, diplomatic, intelligence and technological power that could have been delivered to the tune of “Everything Is Awesome.”

No, the precise moment came in an onstage interview Wednesday at the Economic Club of Washington, D.C., when, after fielding a series of easy queries, he was asked a deceptively deferential one: If he could write his own epitaph, how would he want to be remembered?

History will record and debate his answer: “Defender of Israel, liberator of its economy.”

But it may be more revealing, after 12 years as prime minister in which his name became synonymous with his government if not his state, that Mr. Netanyahu was even asked the question.