At the Al Smith charity dinner, Obama previewed his all-purpose fallback to criticism on international affairs.
"Spoiler alert: We got bin Laden," he said, a reminder of the signature foreign policy triumph of his term, the death at the hand of U.S. special operations forces of the mastermind behind the terror attacks on the United States more than a decade ago.
The president and his challenger agreed long ago to devote one of their three debates to foreign policy, even though opinion polls show voters care most about economic concerns.
Growth has been slow and unemployment high across Obama's tenure in the White House. Romney, a wealthy former businessman, cites his experience as evidence he will put in place policies that can revive the economy.
In recent weeks, the former Massachusetts governor has stepped up his criticism of the president's handling of international matters, although his campaign hasn't spent any of its television advertising budget on commercials on the subject.
In a speech earlier this month, Romney accused the president of an absence of strong leadership in the Middle East, where popular revolutions have swept away autocratic regimes in Egypt and elsewhere in the past two years. He has also accused Obama of failing to support Israel strongly enough, of failing to make it clear that Iran will not be allowed to develop a nuclear weapon and of backing cuts in the defense budget that would harm military readiness.
Yet Romney has stumbled several times in attempting to establish his own credentials.
He offended the British when he traveled to England this summer and made comments viewed as critical of their preparation for the Olympic Games.
Democrats pounced when he failed to mention the U.S. troops in Afghanistan or Iraq during his acceptance speech at the Republican National Convention in late August, and officials in both parties were critical of his comments about the attack in Benghazi while the facts were unknown.