President Barack Obama took a fresh swipe at Mitt Romney Thursday over the leaked video that shows the Republican nominee dismissing 47 percent of Americans, saying the comments suggest Romney probably hasn’t “gotten around a lot.”

Obama made the remarks during an interview in Miami with Univision, the Spanish language network, a day after Romney had given an interview to the same network.

On Wednesday, moderator Jorge Ramos asked Romney to clarify what he meant on the tape. “Well, first of all this is a campaign about the 100 percent,” Romney said. “And over the last several years, you’ve seen greater and greater divisiveness in this country. We had hoped to come back together but instead you've seen us pulled apart. And politics has driven us apart in some respects. So, my campaign is about the 100 percent in America.”

On Thursday, Ramos asked the president: “For you, which is the true Mitt Romney?”

The president seized the opportunity to slam his opponent: “When you express an attitude that half the country considers itself victims that somehow they want to be dependent on government, my thinking is maybe you haven't gotten around a lot.”   

The president then argued that he has a better understanding of the country. “I travel around the country all the time and the American people are the hardest-working people there are. And their problem is not that they're not working hard enough or they don't want to work or they're being taxed too little or they just want to loaf around and gather government checks.”

Romney has been playing defense since the liberal magazine Mother Jones publicized remarks that were secretly videotaped at a Florida fundraiser in May. The video shows Romney telling an audience of wealthy donors that he isn’t concerned about getting the support of nearly half the country because they’re already Obama supporters who are dependent on the government and view themselves as victims.

For the most part, Romney has stood by his remarks, arguing that they highlight the difference between his economic views and the president’s. Romney has tried to paint the president as a big-government liberal; he recently pointed to a videotape from 1998 which shows then-state Senator Obama saying he supports a “redistribution” of wealth. White House Press Secretary Jay Carney suggested the Romney campaign was “desperate” for highlighting a 14-year-old video.

Updated at 8:02 a.m. ET: MIAMI — Mitt Romney said his campaign is about "100 percent" of Americans as his campaign continued to work to contain the fallout from controversial comments he made at a private fundraiser in May.

Romney, speaking Wednesday at a forum sponsored by Spanish-language broadcaster Univision, softened his tone in reaction to a question about his surreptitiously-recorded comments to donors, in which he dismissed 47 percent of Americans as not winnable because of their dependence on government.

"First of all, this is a campaign about the 100 percent. And over the last several years, you’ve seen greater and greater divisiveness in this country. We had hoped to come back together but instead you've seen us pulled apart," Romney said. "I am concerned about the fact that over the past four years, life has become harder for Americans."

Jim Young / Reuters

Republican presidential nominee Mitt Romney arrives at Univision and Facebook's "Meet the Candidates" Forum moderated by Maria Elena Salinas and Jorge Ramos in Miami, Florida, September 19, 2012.

That represented a softer, more inclusive tone for Romney, who dropped language he had used on Fox News and with Republican donors about the comments reflecting the role of government in society.

Later at a rally at an exposition center in Miami, Romney evoked his father, whose bootstrapping history he regularly references on the campaign trail, as an example of someone who benefited from government help without becoming dependent.

"My dad was born in Mexico of American parents living there. At age 5 or 6 there was a revolution. They came back to the United States, and my dad had to get help, financial help. The government helped his family be able to get on their feet again," Romney said. "By the way, that’s the way America works, we have great hearts; we care for people who have needs. We help get them back. We help lift them up but then they go back to their permanent lifestyle. We help people, we get them on their feet and they build a brighter future.”

Romney also laughed off another controversial remark from the leaked tape, in which he told donors about how being a Latino himself might have helped his chances against President Barack Obama. Romney's father was born in Mexico, and a Univision moderator asked him if he was certain he wasn’t Hispanic.

"I think for political purposes that might have helped me here at the University of Miami today," Romney deadpanned.

The event marked a renewed effort by Romney to cut into Obama's sizable advantage with Latino voters. He was softer on immigration, health care and education issues, all the while attacking the president for failing to fulfill his campaign promises to the nation's fastest-growing demographic group.

At the Spanish-language forum, Romney pledged a solution to what he called the nation's broken immigration system. He said he had no intention of "rounding up" the roughly 12 million undocumented immigrants thought to be in the United States illegally while his plan takes shape.

"I said I'm not in favor of a deportation, a mass deportation effort rounding up 12 million people and kicking them out of the country," Romney said. "I believe people make their own choices as to whether they want to go home and that's what I mean by self-deportation. People decide if they want to go back to the country of their origin and get in line legally to be able to come to this country."

'Federal solution'
Democrats have attacked Romney's "self-deportation" concept since the primary campaign, when Romney used immigration as an issue with which to attack his rivals from the right, essentially promising to make economic opportunity so scarce for illegal immigrants that they would leave the United States voluntarily.

Before an almost exclusively Latino audience on the campus of the University of Miami, Romney defended his support for only one provision of a controversial Arizona immigration law and praised legal immigration as key to America's vitality.

"One aspect of the Arizona law which I think is worthwhile to consider and be part of a federal solution is this idea of an employment verification system," Romney said when pressed on his past praise for the Arizona law. Romney said the law would not have been necessary if President Obama had followed through on promises to reform federal immigration laws in his first term.

"The reason there is an Arizona law is because the federal government and specifically President Obama didn't solve the immigration problem when he came into office," Romney said.

With polls consistently showing Romney trailing President Obama by a 2-to-1 margin among Latino voters, the outreach by the former Massachusetts governor here – aimed at all Latinos, but with a particular focus on the Cuban-American community here – is critical.

That might be why Romney, who rarely mentions his Massachusetts health care reform law because of its similarities to the president's health care reform bill, embraced his connection to some of the law's most popular provisions here. Among Latinos, health care has been a key issue.

"I have experience in health care reform," Romney said after vowing to repeal President Obama's healthcare reform law. "Now and then the president says I’m the grandfather of Obamacare. I don’t think he meant that as a compliment but I’ll take it. This was during my primary. We thought it might not be helpful. But I’ve actually been able to put in place a system that fit the needs of the people in my state. And I’m proud of the fact that in my state after our plan was put in place every child has insurance. Ninety-eight percent of adults have insurance, but we didn’t have to cut Medicare by $716 billion to do that."

The Obama campaign quickly responded to the events, accusing Romney of offering only platitudes to the Hispanic community.

"Mitt Romney is wrong on issues of importance to the Hispanic community. On critical issues, he continued to refuse to answer any of the tough questions or provide any specifics on what he’d do as president," Obama campaign spokesperson Lis Smith said in a statement. "We are just two weeks away from the first presidential debate, where the American people will demand more than vague answers and empty platitudes. It’s time for Mitt Romney to come clean and get specific about his policies.”