Obama got Osama.

That's what some people chanted when the news of Osama Bin Laden's killing broke. But will it have any impact on the President Barack Obama's politics and popularity?

Mr Obama has gone out of his way to stress that "get Bin Laden" was his direct instruction and that the arch villain's death is, in part, his victory. White House officials are doing all they can to capitalise on what looks like a mood of nationwide elation.

Any president who "got" Bin Laden would benefit. Former President Bill Clinton's efforts were mocked by George W Bush. Then he failed too, losing Bin Laden in the caves along the border land, as US soldiers stood by.

But perhaps Mr Obama will benefit more than most. His style of decision making is to take time, to deliberate, to chew over every option. His critics call it dithering. There are now some excellent "tick tocks" as they are called here - blow by blow accounts of the decision making process. But you always have to remember all sources are in the circle, and liable to portray the president positively. It sounds as if Mr Obama gave this decision as much time and thought as all the others but away from the public gaze.

Not only did Mr Obama's security advisor John Brennan praise him, but Republicans have even called his decision "gutsy". He did not simply go for bombs or drones but rather a helicopter raid. One insider is quoted as saying that Black Hawk Down was mentioned a few times in the discussions. When that helicopter did go down, Mr Obama surely thought of Jimmy Carter and Iran.

So he's a risk taker, too. It also makes him look focused on what is truly in the US's national interest. You can argue Iraq wasn't, Libya wasn't, even Afghanistan no longer is. But getting the head of al-Qaeda clearly was a number one priority in the minds of many Americans, and Mr Obama decided it was his as well.

Even habitual enemies, indeed even Rush Limbaugh, have praised him. At a reception for Republicans and Democrats last night, he got a standing ovation.

So the wind is behind him. Whence will he sail? At a White House dinner for members of Congress, he used Bin Laden's killing as a call for unity.

He said: "We were reminded again that there is a pride in what this nation stands for, and what we can achieve, that runs far deeper than party, far deeper than politics."

From Bin Laden, he moved effortlessly to domestic public enemy number one, the deficit. "It is my fervent hope that we can harness some of that unity and some of that pride to confront the many challenges that we still face," Mr Obama said.

On Thursday, Mr Obama will travel to New York City to remember those who died in Bin Laden's assault on America. I expect more talk of unity but perhaps some big foreign policy themes as well. There are those who think the halo of success makes it easier for the president to confront a military that wants July's Afghanistan wind-down to be small and fairly insignificant. Others, however, think the momentum runs the other way, and that it gives all the more reason to stay and finish the job.

So the killing sends waves that will wash against these shores and those of a wider world. Some are saying this moment assures Mr Obama's re-election. It assures no such thing.
Apart from the obvious point that there can be many other unexpected events that will have an impact, positive or negative, It just doesn't work like that. However huge this event snow seems, wait a couple of months. In the relentless frenzy of the 24-hour media cycle, it will probably be half forgotten by the the time of the election.

This far out, only events that mean change to people's lives on a day-to-day basis have that sort of game changing impact. But image is important. The president has burnished his in the eyes of many Americans and looks like a resolute commander-in-chief. He knows it, and intends to milk the moment for all it is worth.

The White House has had to correct its facts about the killing of Bin Laden, and for some that has diminished the glow of success that has surrounded all those involved in the operation.

Bin Laden wasn't armed when he was shot. It raises suspicions that this was indeed a deliberate shoot-to-kill operation.

Here are the inaccuracies in the first version. The woman killed was not his wife. No woman was used as a human shield. And he was not armed.

The president's press secretary Jay Carney suggested this was the result of trying to provide a great deal of information in a great deal of haste.

I can largely accept that. There is no mileage in misleading people and then correcting yourself. But the president's assistant national security advisor John Brennan had used the facts he was giving out to add a moral message - this was the sort of man Bin Laden was, cowering behind his wife, using her as a shield. Nice narrative. Not true. In fact, according to Carney this unarmed woman tried to attack the heavily armed Navy Seal. In another circumstance that might even be described as brave.

Jay Carney said that Bin Laden didn't have to have a gun to be resisting. He said there was a great deal of resistance in general and a highly volatile fire fight. The latest version says Bin Laden's wife charged at the US commando and was shot in the leg, but not killed. The two brothers, the couriers and owners of the compound, and a woman were killed on the ground floor of the main building. This version doesn't mention Bin Laden's son, who also died.

By this count only three men, at the most, were armed. I do wonder how much fight they could put up against two helicopters' worth of Navy Seals.

Does any of this matter? Well, getting the fact right is always important. You can't make a judgment without them. We all make mistakes, and journalists hate doing so because it makes people trust us less. For those involved an operation like this, time must go past in a confused and noisy instant, and they aren't taking notes. Confusion is very understandable. But you start to wonder how much the facts are being massaged now, to gloss over the less appealing parts of the operation.

And of course there is the suspicion that the US never wanted to take Bin Laden alive. Here at least many see a trial as inconvenient, awkward - a chance for terrorists to grandstand. Look at all the fuss about the trial of Khalid Sheikh Mohammed.

In the confusion of a raid it's hard to see how the Seals could be sure that Bin Laden wasn't armed, didn't have his finger on the trigger of a bomb, wasn't about to pull a nasty surprise. If he had his hands in the air shouting "don't shoot" he might have lived, but anything short of that seems to have ensured his death.

I suspect there will be more worry about this in Britain and Europe than in the US. That doesn't mean we are right or wrong. It is a cultural difference. We are less comfortable about frontier justice, less forgiving about even police shooting people who turn out to be unarmed, perhaps less inculcated with the Dirty Harry message that arresting villains is for wimps, and real justice grows from the barrel of a gun. Many in America won't be in the slightest bit bothered that a mass murderer got what was coming to him swiftly, whether he was trying to kill anyone in that instant or not.

Thanks for reading this: my blog is moving to a new home. The idea is to bring all my work and analysis together on one page: the blog, of course, but TV and radio pieces and [very soon] my tweets too. It's a great idea, and one the BBC is applying to most of the other editors and correspondents who blog.

I tend to use Twitter to link to either what I've written myself or to the work of colleagues, inside or outside the BBC. But that may change over time, as I see the virtue of live tweeting. The true worth of Twitter was shown on Sunday, when it gave us the first inkling that Osama Bin Laden was dead. Not all the speculation about the details was right but the one huge fact was.

The way I approach Twitter and news on the internet is very much driven by the way I consume it. The built TV bulletin is very far from going the way of the dodo but I want to be able to watch crafted reports online too. This new page should allow this and more.

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