HEMPSTEAD, New York — Barack Obama turned his administration's worst foreign policy disaster into a dramatic victory in Tuesday's debate when Mitt Romney sought to stretch the criticism of the Obama Administration's handling of the incident.

Romney's criticism of Obama's handling of the crisis met a stern lecture from Obama about politicizing the tragedy; and when Obama said he'd called the incident an act of terror from the start, Romney thought he saw an opening.

The Republican attacked Obama for, he said, calling the attack on Benghazi a terrorist attack until two weeks later, only to be interrupted — and corrected — brusquely moderator Candy Crowley, who noted that Obama had used the phrase "acts of terror" in the Rose Garden immediately after the attack.

Republicans later argued that he hadn't specifically applied the phrase to Libya.

"Both the president and the moderator were wrong, said Romney aide Ron Kaufman.

And Republicans signaled they planned to keep fighting over the quote Wednesday.

"He never called it an act of terrorism," said Republican National Committee spokesman Sean Spicer, who conceded that Romney's answer "might be a bit confusing" for people who weren't paying close attention.

"We will be forcefully making sure that the timeline is accurately communicated," he said. "We hope more will come out tomorrow and the media will do its job"

But Democrats welcomed that argument, and the press seems unlikely to give Romney much more leeway than Crowley did on contesting a fairly clear transcript of a presidential event. Obama was in the Rose Garden to speak about Libya, and the context of the quote is not ambiguous — though the broader Republican complaint that the Administration at first labeled the attack the result of a spontaneous protest is accurate.

"When even the moderator fact checks you in front of the audience you, know you've stepped over the line," said Maryland Governor Martin O'Malley, an Obama surrogate.

The blunder — the one moment Tuesday when a candidate seemed genuinely rattled — may have been the product of, if anything, overpreparation.

For weeks, Romney aides have been talking about Libya as a growing issue that would undermine Obama’s lead with voters on foreign policy.

“I’m telling you,” a top Romney aide told BuzzFeed last week, “Obama can’t defend the cover-up.”

But it was Romney who couldn’t defend a patently false attack, and couldn’t navigate to safe ground.

Democrats were so confident in the performance that even before the debate was over they marched in their surrogates in dramatic fashion, answering questions while Romney and Obama answered their final questions.

"We saw a rattled mitt Romney tonight," gloated Obama press secretary Jen Psaki, who called his performance on Libya an "unmitigated disaster. "He doesn't have a bit of credibility on foreign policy issues."