MIAMI (CBSMiami) – After a disastrous first debate, President Barack Obama needed a much stronger performance in the second presidential debate and the early results say Obama got exactly that on Tuesday night.

The debate will be remembered for several things including a moment early on when both candidates got into each other’s faces while discussing issues. One moment that drew applause from the audience, and rankled conservatives, was a fact-check by the moderator, Candy Crowley, on a statement from Republican nominee Mitt Romney.

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Romney said the Obama campaign didn’t condemn the attack in Libya that cost a U.S. ambassador his life as an act of terror. Romney claimed it took two weeks for the president to make the claim that it was a terror attack.

But, Crowley asserted, that in a Rose Garden speech the day after the attack, Obama did label it an act of terror. CNN reported he made a similar comment two days later at a campaign even in Las Vegas when he vowed to bring the killers to justice.

Romney later asserted, “Well, the president took Detroit bankrupt. You took General Motors bankrupt…This was precisely what I recommended and ultimately what happened.”

Romney famously wrote an op-ed that said, “Let Detroit Go Bankrupt,” to voice his opposition to the auto bailout programs. Romney wrote that he completely opposed using government money to bail out the automakers, instead relying on private financed bankruptcy. However, at the time, no private company would give automakers money due to the credit risks and private money wasn’t available, according to

Detroit and the automakers received government bailout money, have been setting sales records ever since emerging out of bankruptcy, and have hired thousands of former workers who were laid off during the Great Recession.

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President Obama had a problem with stretching the truth when he claimed, “And what I want to do is build on the 5 million jobs that we’ve created over the last 30 months in the private sector alone.”

Obama’s statement is technically true, though the actual number of jobs created in the last 30 months is closer to 4.5 million. However, the numbers don’t include the jobs that were being hemorrhaged as Obama took office and in his first three months in office, which totaled about 4.3 million jobs.

The numbers have been a focal point of both campaigns throughout the election. The Romney campaign long sought to have the president’s job creation count start from January 2009, when the economy was still shedding millions of jobs.

Romney’s campaign argued that when looking at his job record in Massachusetts, that the jobs numbers shouldn’t start counting until his policies went into place. Using that metric, Obama’s close to the truth in his statement as millions of jobs have been created since the stimulus was enacted in late March 2009.

According to the snap polls after the debate, Obama won in a CNN poll by seven points. A CBS poll of undecided voters revealed a similar outcome:

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A battleground poll during the debate found Obama up 53-38 percent thanks to Tuesday’s performance.