So, while all of you doubters retire to your fainting couch, clutching your pearls, the back of your hand to your furrowed brow, let me point out a few things.

1. GOADING PRESIDENT OBAMA INTO BECOMING ANGRY AND DEFENSIVE WAS IN MITT ROMNEY'S GAME PLAN
Check this out from the September 28, 2012 New York Times piece where they talked about Mitt Romney's debate strategy and how he was preparing "zingers" to unleash during the debate:

Mr. Romney’s team has concluded that debates are about creating moments and has equipped him with a series of zingers that he has memorized and has been practicing on aides since August. His strategy includes luring the president into appearing smug or evasive about his responsibility for the economy. {...}

During rehearsals, Mr. Romney has tried lines of attack suggesting that Mr. Obama distorts the facts and sloughs off responsibility on others. Mr. Romney’s aides recall Mr. Obama’s tart “you’re likable enough” line to Mrs. Clinton in 2008 and hope to goad him into a similarly churlish moment. Mr. Romney will win, the advisers said, if he can force Mr. Obama to come across as condescending or smug.

Romney's strategy was to make President Obama look defensive and angry. Because nothing plays worse in Anti-Obamaland than the Angry Black President. If you are trying to win over all of those white people -- and Mitt Romney MUST win like 60+% of the white vote -- he's got to try to make President Obama seem hostile and angry to white people.

So, President Obama kept his cool. He allowed the lies and attacks to wash over him and remained calm, not responding with emotion, something that could lead him to say something intemperate.