President Obama sought Thursday to capitalize on opponent Mitt Romney’s rough week, saying the GOP nominee is out of touch if he stands by his caught-on-camera moment calling many voters “victims” who are dependent on government.

“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 said at a forum with Spanish-language network Univision in Miami.

In the forum, Mr. Obama took heat for failing to pass an immigration bill and fended off tough questions about American intelligence and security in the wake of last week’s attacks on diplomatic posts.

While Mr. Obama seized on Mr. Romney’s unguarded moment, the Republican candidate returned the favor, saying a 1998 audio clip of Mr. Obama saying he supports using government to redistribute wealth, which surfaced this week, underscores what’s at stake in this year’s election.

He also criticized Mr. Obama for saying at the forum that Washington cannot change itself and must be forced to change from the outside.

“Well, we’re going to give him that chance in November,” Mr. Romney said. “He’s going outside. I will change Washington. We’ll get the job done from the inside — Republicans and Democrats will come together. He can’t do it.”

The back-and-forth comes as Gallup’s polling shows Mr. Obama’s post-convention high has evaporated and the race now stands at a dead heat. Some other polls, though, show Mr. Obama doing well in key battleground states.

Pundits argued this week that Mr. Romney hurt his chances by appearing to write off half of the electorate when he said 47 percent of voters don’t pay income taxes, take government benefits and see themselves as victims, and that he wasn’t going to win their support.

Mr. Obama capitalized on the “47 percent” meme Thursday at the Miami town-hall meeting.

“The day I was elected … I said 47 percent of the people didn’t vote for me, but I’ve heard your voices, and I’m going to work just as hard for you as for those who did vote for me,” said Mr. Obama, who coincidentally did win 53 percent of the vote in 2008.

“That’s how you have to operate as president. 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,” he said. “People want a hand up, not a handout.”

He said the roughly 47 percent of Americans who don’t pay federal income tax still pay such other levies such as sales taxes, state and local taxes, and payroll taxes.

“Americans work hard, and if they’re not working right now, I promise you, they want to get to work, and that’s what my economic plan is designed to do,” Mr. Obama said.

Mr. Obama also said there are lots of millionaires who abuse the tax system, too.

“Are there people who abuse the system? Yes, both at the bottom and at the top,” Mr. Obama said. “Because there are a whole bunch of millionaires who aren’t paying taxes at all, either.”

The critique was a two-fer for the president, enabling him to remind voters that the millionaire Republican nominee has paid a relatively low effective tax rate of 13.9 percent in 2010 and won’t release more than two years of his tax records, while also bolstering Mr. Obama’s campaign theme that Mr. Romney is out of touch.

The president spoke at length at the Univision event about immigration, acknowledging that he broke a 2008 campaign promise to enact comprehensive immigration reform in his first year in office. He blamed Republican lawmakers for not cooperating, saying he was “naive” in not anticipating that they would walk away from him.

“I am the head of the executive branch,” Mr. Obama said. “I am not the head of the legislature. We’ve got to get cooperation.”

Mr. Obama also said he made the promise about immigration legislation in May 2008, before he knew how bad the recession would turn out to be, and that preventing another Great Depression became his priority once he got into office.

“I did not make a promise that I would get everything done, 100 percent,” Mr. Obama said. He pointed out that he took executive action this year to stop young illegal immigrants from being deported, and said he will push for reform legislation again after the elections, when he hopes Republicans will be more cooperative.

As if acknowledging his ineffectiveness, Mr. Obama said at one point, “The most important lesson I’ve learned is that you can’t change Washington from the inside. You can only change it from the outside.”

That prompted Mr. Romney’s rejoinder about sending Mr. Obama home from Washington. Mr. Romney said the president’s comments showed he’s out of ideas.

“He can’t do it. His slogan was ‘Yes, we can.’ His slogan now is ‘No, I can’t.’ This is time for a new president,” the Republican said.

At the forum, Mr. Obama addressed the anti-U.S. protests at diplomatic posts in the Middle East, saying that he now thinks the attack on the consulate in Libya, which killed four Americans, was a terrorist act.

Since the assault on Sept. 11, the administration has been saying that the attack was in response to an anti-Islam movie filmed in the United States.

“The natural protests that arose because of the outrage over the video were used as an excuse by extremists,” Mr. Obama said. “This is part of the reason why we have to remain vigilant. Those forces have not gone away.”

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