Obama, Romney debate at Hofstra (VIDEO)

NEW YORK – President Barack Obama and Republican challenger Mitt Romney faced off in a town hall-style debate at Hofstra University on Tuesday night, covering topics from the economy, taxes, income inequality and jobs to immigration, gun control and energy independence.

Obama's goal for the night was to overcome his previous debate performance, where he admitted, "I had a bad night," according to the Associated Press.

The moderator of the debate, Candy Crowley of CNN, said she expected to ask follow up questions, but both campaigns drafted a formal memo stating that her role should be limited. The questions in the debate were gleaned from around 80 undecided voters inside the hall, said the AP.

The debate started off with the biggest concern of this election: the economy.

The first question came from a soon-to-be college graduate concerned about getting a job after graduation. Romney reiterated that the middle class has been crushed over the past four years, while referring to a five-point plan. "I know what it takes to keep this economy going," he said, though he did not provide details.

Obama also laid out five points for his economic plan, which he said included increasing manufacturing jobs, improving the education system, achieving energy independence, reducing the deficit and rebuilding American infrastructure.

The candidates engaged each other much more aggressively as compared to the previous debate in Denver, especially on the topic of gas prices and energy independence. Romney said, "I will fight for oil, coal and natural gas," while stating that the Obama administration would not.

Obama responded with, "I'm all for pipelines, I'm all for oil production, what I'm not for is ignoring the other half of the equation." He said energy independence should also include exploring renewable resources such as solar and wind power.

When Romney said, "[Oil] production on government land is down," Obama retorted, "No it isn't. That's just not true."

Economic concerns dominated the questions of the night, with the next audience member asking about Romney's tax plan. Romney said, "The reason I want middle-income taxpayers to have lower taxes is because middle-income taxpayers have been buried over the past four years."

Obama hit his stride during the question about tax rates, responding to Romney's tax plan with: "You can't buy the sales pitch. Nobody who's actually looked at [Romney's tax plan] thinks it actually adds up."

Romney insisted that of course the numbers added up. The Obama campaign has pointed to the lack of detail in Romney's tax plan with this ad.

The next question focused on addressing inequality at the workplace, specifically for women who made less than their male counterparts. Both candidates insisted that they cared about women, with Obama again reminding voters that the first act he signed in office was the Lilly Ledbetter Act.

"This is not just a health issue, it's an economic issue for women," said Obama, tying equality in the workplace to women's right to access contraceptives and health care.

The next question came from an undecided voter who was concerned about former President George W. Bush's legacy and asked Romney how his presidency would differ from Bush's. Romney said he would diverge from the Bush administration on China, energy policies and the deficit, stating, "I'm going to get us to a balanced budget. President Bush didn't."

Obama made the case that Romney had moved even farther right than Bush on social issues.

More on GlobalPost: Presidential debate: A 3-point China primer for the second showdown

When the debate turned to trade, Obama said, "Governor, you're the last person to get tough on China," claiming that Romney's company invested in companies that outsourced jobs to China.

Romney reiterated that he would get tough on China and name it as a currency manipulator. "The middle class is getting crushed under a president who doesn't understand how to get this economy working again," said Romney.

As the debate turned to immigration, Obama said talent from around the world wanted to come to the United States, but he was in favor of regulating immigration. He pushed back on Romney's support of the Arizona immigration law, which would allow police to check the documents of anyone who they suspected to be an illegal immigrant.

Obama reminded voters that Romney wanted to make conditions for immigrants so miserable that they would self-deport.

Romney shot back, "I'm not in favor of rounding people up and taking them out of this country."

The first and only foreign policy question of the night was on the topic of the attack on the US consulate in Benghazi, which led to the deaths of four Americans, including US Ambassador Chris Stevens. Obama defended his administration's response staunchly, saying, "You don't turn national security into a political issue. Especially not right when it's happening."

Romney pressed Obama on the timeline of events and on the charge that a request for extra security at the consulates in Libya had been turned down, in what turned out to be perhaps the most spirited portion of the debate.

"The suggestion that anybody on my team would play politics or mislead when we've lost four of our own is offensive," said Obama.

When Romney was pushing the point that the Obama administration had refused to label the Benghazi attack an act of terror, Obama said he had called it that the day after the attack. In a rare moment of live fact-checking, moderator Crowley was able to confirm that Obama had in fact referred to the attack as an act of terror.

A day after Secretary of State Hillary Clinton accepted responsibility for the embassy security request in Libya, Obama said, "I'm the president, and I'm always responsible."

By the end of the night, the consensus seemed to be that Obama had held his own this time, though Romney had not lost much. Both candidates engaged each other forcefully, disagreeing on each other's facts, policies and campaign promises. The next debate will focus on foreign policy.

More on GlobalPost: President Barack Obama and Mitt Romney: the Hofstra showdown (LIVE VIDEO)