But it is the Gallup poll that remains Trump’s great unrequited love. Nearly every day since the presidency of Harry Truman, the opinion-research firm has asked a scientific sampling of the American electorate the same question: “Do you approve or disapprove of the way [name] is handling his job as president?” And over the past year Gallup has found Trump, with unpitying consistency, the least-approved-of president in the history of its polling. In mid-February, his numbers ticked back up, to 40 percent — but that is still well short of the 57 percent who disapprove of him.

He is not the first modern president to obsess over these ratings, but the nature of his obsession is different. Presidents from Lyndon Johnson to George W. Bush spoke bluntly about approval as a means to an end. For Trump, approval seems to be the end. His primary pre-presidential business was, quite literally, being popular, and now that he is in the White House, mass approval is the one thing that is consistently denied to him. There is something oddly poignant about the R.N.C. email polls; they’re like the birthday card that a middle manager hustles the hourly employees to sign for a company president who everyone knows has just gone through a rough divorce.

What’s most bizarre about this particular manifestation of Trump’s exhausting, relentless need for external affirmation, though, is how ill placed it is. No president has ever been so publicly consumed with his approval numbers. And no president has ever had less reason to care about them.

What does it mean, exactly, to “approve” of a president? Does it mean you like Trump enough that, if there were an election tomorrow, you would vote for him? Does it mean that you like him personally? Or does it mean that you don’t like him personally but think that he’s handling affairs of state well enough anyway?