The Romney campaign seeks to make the Libya attack a major campaign issue to try to cut into Obama's advantage over Romney on foreign policy issues, according to polls.
The third and final presidential debate next Monday in Florida will focus on foreign policy.
Both candidates walked the floor with microphones in hand during the 90-plus minute debate on Tuesday, raising their voices at times and repeatedly challenging each other's points.
Crowley tried in vain at times to prevent each man from going over allotted time, with Obama speaking for more than three minutes longer than Romney overall. However, a count by CNN showed that for the second straight debate, Romney spoke more words despite talking for a shorter time.
Obama was on the attack from the start, but waited until his final answer -- with no chance for Romney to respond -- to raise his opponent's controversial "47%" comments at a fundraiser in May.
In remarks made public by a secretly recorded video of the event, Romney described 47% of the country as people dependent on government aid who refused to take personal responsibility. The president was criticized after the first debate for not raising the issue and he made sure to do so this time.
"Think about who he was talking about," Obama said, listing people on Social Security "who've worked all their lives," veterans "who've sacrificed for this country," students, soldiers and "people working hard every day."
The president said he wanted to fight for those people "because if they succeed, I believe the country succeeds."
Earlier, Obama went after Romney's five-point economic plan that the GOP candidate repeated two times during the debate, saying it really was a one-point plan "and that plan is to make sure that folks at the top play by a different set of rules."
Romney shot back that "if you elect President Obama, you know what you're going to get -- you're going to get a repeat of the last four years."
Over and over, Romney described what he called the failings of Obama's policies including rising federal deficits and debts, more than 20 million people unemployed and anemic economic growth.
"We don't have to settle for what we're going through," Romney said at one point. "We don't have to settle for gasoline at four bucks. We don't have to settle for unemployment at a chronically high level. We don't have to settle for 47 million people on food stamps. We don't have to settle for 50 percent of kids coming out of college not able to get work. We don't have to settle for 23 million people struggling to find a good job."
Obama was "great as a speaker, but his policies don't work," Romney said. Attempting to rebut Obama's criticism of his own policies, Romney insisted he would prioritize middle class growth, saying "it's about how we can get the middle class of this country a bright and prosperous future."
However, Romney failed to provide further specifics of his tax policy, even when one audience member asked about unspecified deductions and loopholes the candidate says he will eliminate.
A CNN/ORC International poll of people who watched the debate indicated that 46% thought Obama won, compared to 39% for Romney. The result was within the survey's margin of error, and responses to other questions showed debate watchers favored Romney on the economy and other major issues.
After the first debate on October 3, a similar poll showed Romney scored a solid victory in the eyes of more than 60% of respondents.
"Most improved -- that award goes to Barack Obama," CNN Senior Political Analyst David Gergen said.
Daily Beast's Andrew Sullivan, who called Obama's poll numbers after the first debate "devastating," predicted the president would come "kicking back in the polls" in coming days.
Erick Erickson, the conservative RedState.com blogger and CNN contributor, thought Romney won the debate based on "clear majorities outside the margin of error" in the CNN/ORC poll who thought Romney would be better for the country on economic issues.
"In fact, while other areas of the debate may overshadow this point, Romney deftly dispatched Obama on his economic record," Erickson said, calling it "the one issue that matters."
An awkward phrase by Romney in addressing gender pay inequality was creating the most buzz around the debate.
Romney said when he was elected governor of Massachusetts, all the applicants for cabinet positions were men, so he sought out women applicants. "I went to a number of women's groups and said, 'Can you help us find folks?' and they brought us whole binders full of women."
Before the debate was over "binders full of women" had a Twitter hashtag, a series of memes on Tumblr, and a Facebook page with over more than 100,000 fans. The phrase was the third-fastest rising search on Google during the debate.
Unlike the first presidential debate, the town hall-style format allowed audience members to ask the questions. Crowley, the first woman to serve as moderator of a presidential debate in 20 years, tried to get in as many of the questions as possible from the uncommitted voters in the hall, sometimes struggling to cut off the candidates as they tried to make points or argued with each other.
Questions addressed troubles finding jobs, tax policy and immigration, with Romney saying Obama failed to deliver on a promise to pass a major immigration overhaul while the president said Romney backed conservative positions such as opposing a measure that gives some children of unregistered immigrants a path to legal status.