ABC News' Matthew Larotonda has the facts:
Independent fact check organizations have poured over the rhetoric of diplomatic apologies repeatedly during this election, and the results have been mostly in opposition. Most recently the governor has brought it into reference of the administration's response to the attack on the U.S. consulate in Libya.
Further back, the idea of an Obama "apology tour" has been a recurring attack for conservatives for a long time and has its roots in diplomatic travel the president undertook in 2009 shortly after taking office. Romney himself first took up the phrase in 2010 with his book, "No Apology: The Case for American Greatness," and has repeated the theme continuously on the campaign trail.
"In his first nine months in office, President Obama has issued apologies and criticisms of America in speeches in France, England, Turkey, and Cairo; at the CIA headquarters in Langley, Va., the National Archives in Washington, D.C., and the United Nations in New York City," the book reads in its first chapter.
President Obama never formally regrets American policy during these speeches, rather taking a tone of reciprocal blame at times for diplomatic ties that may have been strained. At other times the president is drawing a distinction between his policies and those of his predecessor, President George W. Bush.
During the 2009 Cairo speech for example, Obama comes close to regretting American actions in Iran during the overthrow of the Shah. But he immediately counters by pointing the finger at subsequent regimes for continued hostility.
"In the middle of the Cold War, the United States played a role in the overthrow of a democratically elected Iranian government," he said. "Since the Islamic Revolution, Iran has played a role in acts of hostage-taking and violence against U.S. troops and civilians. This history is well known."
On his first visit to France, Obama again seemed to take responsibility for declining attitudes toward Americans abroad, for policies that have shown "arrogance and been dismissive, even derisive." But on the flip side he immediately derided Europeans for "casual" and "insidious" anti-Americanism.
"On both sides of the Atlantic these attitudes have become all too common," he said. "They are not wise. They do not represent the truth. They threaten to widen the divide across the Atlantic and leave us more isolated."
All of these remarks fall short of formally apologizing for American diplomacy, but some of the president's most conciliatory remarks have come regarding the detainees of Guantanamo Bay. At the 2009 National Archives speech on terrorism, Obama said the military prison's use was "based on fear than foresight," and that "it likely created more terrorists around the world than it ever detained."
Click to read ABC News fact checking of entire final presidential bebate