Matthew Norman: Obama has shown the world why it fell in love with him

What seemed a cutely sculpted ironic punchline at the moment of delivery looks, with hindsight, like the joke of the millennium so far – and with only 989 years to go, it will take some beating.

Barack Obama's Saturday night turn at the White House Correspondents' Dinner was a masterpiece, its biggest laughs involving a cross-looking Donald Trump. Apologies if you've seen it, but after dwelling on a Celebrity Apprentice episode in which the team's cooking failed to impress the folks from Omaha Steaks, Obama recounted how Trump identified the problem as one of leadership. The Donald spared two celebs, related the Prez, including Meatloaf, but fired the eccentric actor Gary Busey. "And these are the kinds of decisions," he went on, "that would keep me up at night." How he staved off the frantic giggles as he imagined the sleepless night to come, I've no idea. But no flicker in the eyes hinted at a pending decision behind imminent insomnia, and the first thought on reviewing the gag is that you really, really wouldn't want to play poker with this guy.

Obama is said to be a strong player in the tight-aggressive style, which means that he doesn't play a lot of hands or bluff much; but that when the potential return justifies the risk, he isn't scared to push all his chips in.

This is what he did in Abbottabad 24 hours later... and doesn't the hi-tech, surgical strike viewed "in real time" back at the White House have a thrillingly 24-ish feel (albeit without one of Bin Laden's daughters in the situation room sabotaging Bajack Obauer's efforts)? Cruise missiles are sooooo 2007.

He bet the lot – his presidency, re-election chances, and place in history – on what, we may assume, was a virtual coin flip. The odds on the mission's success are unquantifiable, but when his counter-terrorism adviser, John Brennan, described this as "one of the gutsiest calls of any president in recent memory," he strayed towards understatement. Had it gone wrong, Obama would by now have been measured up for the Jimmy Carter One Term Memorial Shroud. If Bin Laden had escaped and the Navy Seals been killed, his announcement that he had revived al-Qa'ida with its finest propaganda coup since 9/11 would have moonlit as his own political last rites.

It did not go wrong, and so he finally became the President of the United States of America, rather than President of That Chunk Of America That Doesn't Regard A Black Man In The Oval Office As The Cleaner Or An Imposter.

The unity may not last, or guarantee the second term. Insta-cliché reminds us of the elder Bush's decline from 1991 war hero to 1992 election loser, and that in 2012 it will more than ever be the economy, stupid. Even so, when Rush Limbaugh says "Thank God for President Obama", you needn't be a genius analyst to sniff out change we can all believe in.

But Obama did more than quell the screechings of the wingnuts, chat-show rabble-rousers, the Birthers and those we should term the Placentas (the After-Birthers who have now progressed to post-certificate conspiracy theories to question his legitimacy). He reminded the world why it fell in love with him in the first place.

It was never solely about the southern preacher oratory. However soaring, that would not have worked had it not been underpinned by the sense that he had the intellect, judgement and temperament to transform the waffle about change into concrete fact. He made many promises, as candidates do, and along with universal healthcare and the widely attacked pledge to take out Bin Laden, even if it took unlicensed sorties into Pakistan, was the vaguer line he spoke in his victory speech in that Chicago park. To those watching at home and around the world, he said, "a new dawn of American leadership is at hand".

After two years of hawkish foreign policy barely distinguishable from his predecessor's, he has made good on that promise – not just with the killing of Bin Laden, but by its manner. All the expert advice, we read, was to do what the Bushes, Clinton, Reagan and all other leaders in memory, recent or otherwise, would have done, which is flatten the compound and its environs with missiles. In making the identification of Bin Laden more difficult, that carried its own risks. But a Carteresque fiasco was incomparably the greater political danger, while from all we know about oxymoronic "smart bombs" many innocents would have died and been maimed.

That was the safe call, and the pressure on him to make it must have been colossal. Yet he saw a harder but better way, and who can blame him for subsequently boasting how he first redefined the CIA's imperative as finding Bin Laden; and then conceived and oversaw the operation himself?

People have criticised him for being "professorial" as well as arrogant. They will do so no longer. He pondered for months, studied the research, weighed up the evidence, and reached the right conclusion. This is one cool, tough prof, and the lesson he has taught by example won't quickly be unlearnt. In asymmetric warfare against a stateless enemy, invading sovereign states and slaughtering civilians is not the way to go. You don't punish the guilty by killing the innocent. You do so by killing the guilty.

If that sounds childishly simple, it defeated the simpleton Bush and his brutish cabal as they confused two-bit fake patriotism with American self-interest, and indiscriminate crusader cruelty with military wisdom. Let no one hear attempts to share Obama's credit with Dubya without revulsion. He failed pitifully in this, as in almost every thing else, and even if waterboarding a key al-Qa'ida operative helped to identify the courier, it cannot begin to justify holding boys of 14 and senile 89-year-olds at Guantanamo Bay. Guantanamo remains open. Obama hasn't honoured on every promise, nor will. He is not the Messiah, although if the Kool Aid truck has redelivered at last, make mine an octuple. For tempering vengeance with mercy, by refusing to reckon countless civilian lives a price worth paying to safeguard himself, hedeserves to sleep easy in his bed, and leave all the sweaty 3am angst to Donald Trump and the other malevolent midgets who will nevertrouble him again.