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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.”