You could hardly blame Barack Obama for looking weary, a little numb, as he responded to the slaughter of at least 50 unsuspecting people at an Orlando gay club.

Another mass shooting on his watch, this one the worst in his country's history. Another hurdle in trying to persuade fellow Americans not to retreat into their respective corners, not to fear people who do not look like them or share their religion. Another list of victims' families to console, while agonizing over his own inability as the most powerful person in the world to spare them their grief.

You would like to think anyone would hate to be president of the United States at a moment like that. But on the available evidence, you would be wrong. Because there was one of the two people with a chance to replace Mr. Obama in a matter of months gloating, practically while the bodies were still warm.

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Donald Trump managed to restrain himself for a few hours, to express horror like a normal human being, before his excitement at the shooter being Muslim and apparently IS-inspired got the better of him.

"Appreciate the congrats for being right on radical Islam terror," the presumptive Republican nominee Tweeted. He didn't want such adulation, he added, just "toughness and vigilance." But, hey, who was he to turn down a golden opportunity to make this about his own vindication?

"I said this was going to happen," he boasted in a sloganeering statement later the same day, because "our leaders are weak." Only he would spare Americans such horrors, because he is not "politically correct" and would restrict Muslims from entering the country.

It was narcissistic. It was opportunistic. It was not how a normal, measured, reasonably empathetic pursuer of public office reacts to tragedy. It was certainly not "presidential," in the way that Mr. Trump's campaign falsely claimed he would be after securing the Republican nomination.

But the scary part, for those who worry about how Mr. Trump would react to a domestic attack if he had his hands on his country's arsenal rather than just a Twitter account, is that events like Sunday's may persuade millions of Americans that "presidential" is not what is needed in their next president.

Presidential, as Mr. Obama has embodied the term, means rising above the fray, appealing to better angels, recognizing and embracing the country's complexities rather than trying to bull through them. It means keeping a level head, at times when that might sound dispassionate to people who are angry and frightened.

"Over the coming days, we'll uncover why and how this happened, and we will go wherever the facts lead us," Mr. Obama said on Sunday. It is hard to imagine many past presidents saying otherwise while police were still investigating the crime scene. But it probably sounded complacent to some ears while Mr. Trump was repeating an unverified rumour that the shooter had screamed "Allah hu Akbar" while opening fire.

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Hillary Clinton might not be as cool as Mr. Obama, and she is somewhat more hawkish in her outlook on how to keep Americans safe, but the presumptive Democratic nominee's instincts in the face of tragedy are not too far from his. Like the President, she declined on Sunday to take Mr. Trump's bait by referring to "radical Islam." (Mr. Trump said they should both step aside for failing to utter those specific words.) Her brief statement hit most of the same notes as Mr. Obama's more eloquent one – about vigilance while remaining true to American values, support for the LGBT community, about continuing to push for gun control.

That last point was as close as Mr. Obama and Ms. Clinton came to advancing their own agenda in response to what happened in Orlando. But like everything else they said, it was tinged with sadness and frustration, in this case at how Republicans have blocked even mild attempts at firearms restrictions – ones that, say, might have prevented an unstable man who had been investigated twice from legally buying an assault weapon and mowing down 50 people.

Even setting aside that most of Mr. Trump's supporters probably oppose tighter gun rules, such talk might have struck them as impotent. Here were Mr. Obama and Ms. Clinton lamenting that they have not been able to do what polite society thinks they should. And here was Mr. Trump, promising to do what polite society thinks he should not, and demonstrating with his behaviour that he meant it.

That Mr. Trump plays by no existing rules of political behaviour – that it is always about "I" rather than "we," and that this somehow demonstrates he would never take no for an answer on anything – is at the centre of his pitch that he would reverse an empire's decline caused by playing by the rules too much. It has worked well enough for him so far, so there is little reason to believe he will suffer for trying to make a day that Americans were feeling extra vulnerable all about himself.