TWENTY-FOUR hours after the American compound in Benghazi was attacked and our ambassador murdered, the tragedy seemed more likely to help President Obama’s re-election campaign than to damage it.

The White House already enjoyed more public credibility on foreign policy than on almost any other issue. When Mitt Romney reacted to the attack with a partisan broadside, portraying a news release sent out by the Cairo embassy before any violence began as a White House apology to the attackers, the president’s path forward seemed clear. He would be disciplined and careful, show anger and steel but also coolness under pressure, and let the rally-round-the-flag effect do its natural work.

What happened instead was very strange. Having first repudiated the embassy’s apology to Muslims offended by a movie impugning their prophet, the Obama administration decided to embrace that apology’s premise, and insist that the movie was the crucial ingredient in the Sept. 11 anniversary violence.

For days after the attack, as it became clearer that the Benghazi violence was a Qaeda operation rather than a protest, White House officials continued to stress the importance of the “hateful” and “disgusting” video, and its supposed role as a catalyst for what Susan Rice, the ambassador to the United Nations, insisted was a spontaneous attack.

This narrative was pushed on Sunday morning programs, on late-night talk shows and at news conferences, by everyone from Rice to Hillary Clinton to the president himself. When Obama spoke at the United Nations shortly after the attacks, the video was referenced six times in the text; Al Qaeda was referenced only once.

Eventually, the White House let the video slip quietly out of its public rhetoric, and refocused on terrorism instead. But everything else that’s come out about Benghazi has seemed much more damning because the administration practiced a strange denial at the outset. The missed warnings, the weaknesses in security, the drip-drip of detail unspigoted by reporting and Congressional hearings — all of it would have been received differently if the White House hadn’t spent a week acting as if it had something big to lose by calling terrorism terrorism.

What explains this self-defeating strategy? One possibility is that Romney’s oft-repeated “apology tour” charge is right, and this White House can’t resist the urge to appease our enemies when America comes under attack. But Romney’s portrait of Obama as Neville Chamberlain has always been just a caricature, and nobody who watched the Democratic convention should doubt Obama’s comfort wrapping himself in the mantle of the war on terror.

Another, more plausible possibility is that precisely because this White House wants to be seen as tough on terrorism, it’s loath to acknowledge the possibility that it doesn’t have Al Qaeda completely on the run.

But even this seems insufficient to explain the White House’s Benghazi blundering. Surely acknowledging the persistence of Al Qaeda wouldn’t undercut the administration’s (justifiable) boasts about having taken out its leader. Indeed, if Bin Laden’s organization is still with us, why wouldn’t Americans want to keep the president who gave the Abbottabad order so he could finish the job?

Perhaps, then, the real explanation for the White House’s anxiety about calling the embassy attack an act of terror has less to do with the “who” than with the “where.” This wasn’t Al Qaeda striking just anywhere: it was Al Qaeda striking in Libya, a country where the Obama White House launched a not-precisely-constitutional military intervention with a not-precisely-clear connection to the national interest.

In a long profile of President Obama published last month by Vanity Fair, Michael Lewis suggested that the president feared the consequences of even a single casualty during the Libyan incursion, lest it create a narrative about how “a president elected to extract us from a war in one Arab country got Americans killed in another.”

How much more, then, might the president fear a narrative about how our Libyan intervention helped create a power vacuum in which terrorists groups can operate with impunity? That’s clearly happened in nearby Mali, where the ripple effects from Muammar el-Qaddafi’s overthrow have helped empower a Qaeda affiliate. In this context, it’s easy to see why the administration would hope that the Benghazi attack were just spontaneous mob violence rather than a sign of Al Qaeda’s growing presence in postintervention Libya as well.

The only good news for Obama in this mess is the fact that Romney, always intent on projecting toughness, hasn’t attacked the original decision to go to war in Libya, or tied the intervention itself to Al Qaeda’s North African advances.

If the Republican nominee were less reflexively hawkish, the White House might be facing the more comprehensive critique that it deserves — and the story wouldn’t be about just the specifics of Benghazi, but also the possibility that Obama’s entire policy in the region has put American interests and lives at risk.