In his pursuit of the Republican nomination, Mitt Romney took an aggressive position on immigration, denouncing the Dream Act, suggesting illegal immigrants should “self-deport” and attacking rivals who appeared to show compassion for some undocumented immigrants.

That has left the presumptive nominee in a deep hole with Hispanic voters, trailing President Obama by more than 40 points among this critically important constituency in the latest NBC News-Wall Street Journal poll. The question is whether Romney can credibly undo the damage from the primaries without igniting a renewed debate about his consistency on the issues.

The problem is clearly on Romney’s mind, so much so that he addressed it openly Sunday at a Florida fundraiser. There, he told his audience that Republicans must do a better job of attracting Hispanic votes and, according to NBC News and the Wall Street Journal, said polling showing Obama far ahead among Hispanic voters “spells doom for us.”

The Hispanic vote will be crucial in many states this fall, from Mountain West battlegrounds — Colorado, Nevada and New Mexico — where the election could be determined, to states such as Florida and Virginia that will be among the most competitive in the nation.

Romney’s Friday schedule reflected those concerns. In Arizona to speak to state chairs of the Republican Party, the former Massachusetts governor included on his agenda a roundtable with Hispanic business leaders.

Immigration is a prime example of how Romney was forced to the right in his battle for the nomination. Faced with a potentially strong challenge from Texas Gov. Rick Perry, he attacked Perry for his support of a state law providing in-state college tuition to children of illegal immigrants who are Texas residents. “It makes no sense at all,” he said in a Florida debate.

Later, he went after former House speaker Newt Gingrich for saying that illegal immigrants who have lived in the United States for a quarter-century or more and who have deep roots in a community should be given an opportunity to achieve legal status but not citizenship. Romney called that a form of amnesty that would “create another magnet” for more illegal immigration.

Romney advisers say their candidate’s focus on the economy will help boost his standing with Latinos. “I think that our goal in this campaign is to focus very intently on the economy,” said Kevin Madden, an outside adviser to the campaign. “When we do, I think that Hispanic voters are going to see that they have a better chance for a brighter future for a President Romney than they have witnessed the last four years under President Obama.”

Obama campaign advisers are determined not to let Romney pivot away from some of his past remarks without challenging him as inconsistent or insincere. They say the record from the primary campaign will be difficult to erase or minimize. “I think it’s an impossible image to reverse,” said Joel Benenson, the Obama campaign’s chief pollster.

Stephanie Cutter, Obama’s deputy campaign manager, said Romney would have trouble turning back the clock with Hispanic voters. “They tuned in at much higher levels during the Republican primaries as a result of the harsh rhetoric, and his positions on everything from the Arizona law to self-deportation didn’t go unnoticed,” she said.

Arizona has been ground zero for a national debate over how to deal with illegal immigration, particularly since the passage in 2010 of legislation that requires police officers to check the immigration status of anyone arrested or stopped, if there is reason to suspect that the person is in the country illegally.

The law generated national controversy, with supporters saying it was necessary because the federal government had failed to secure borders. The Obama administration sued the state of Arizona to block key provisions of the law. Next week, the Supreme Court will hear oral arguments in the case.

On Thursday, Sen. Marco Rubio (R-Fla.), a possible candidate to become Romney’s vice presidential running mate, said, “I do not believe that laws like Arizona’s should be a model for the nation.” But Rubio said he believed Arizona was within its constitutional rights to enact the law.

Romney has said that he supports the law and that he would drop the federal lawsuit if elected. It was widely reported after a Feb. 22 Republican candidates’ debate in Arizona that Romney had described the tough law as a model for the nation. His campaign has since said his reference to Arizona as a model was to a law calling for employers to use an electronic system to verify the legal status of workers, not to the broader legislation.

Asked whether Romney thinks the controversial Arizona law also should be a template for other states, a spokesman, who declined to be identified in order to offer fuller comment, said, “The impact of illegal immigration differs from state to state, as do questions of how to allocate scarce law enforcement resources. Decisions on whether to adopt such laws should be left to the states, so the Arizona law is not a model for the nation.”

When it was passed, Romney said the law should be implemented with care. Arizona Gov. Jan Brewer (R), who endorsed Romney just before the Feb. 28 primary, said Thursday that she had never spoken with Romney about his views on the law.

“I’ve never asked him,” she said. “I know what he has said at the presidential debates, I’ve read a few comments and stuff, so you know, I believe what he says is that he understands the issues and that he realizes that we’ve got to get a secure border,” she said.

“What Governor Romney has said is that model seems to have worked for Arizona, but that doesn’t mean it’s a model for the country or other states,” said Jose Fuentes, co-chairman of Romney’s National Hispanic Steering Committee.

Fuentes said Romney has had a deliberate strategy to be supportive of Arizona’s efforts without endorsing the law outright or ever suggesting that it is a model for the nation.

The GOP’s inability to win stronger support from Hispanics is a long-running problem. Rubio, a Cuban American, is one of a number of Republicans who have argued that the party needs a new strategy to overcome a deficit that has long-term implications.

He is drafting what he hopes will be a compromise version of the Dream Act, which would be more restrictive than the Democrats’ plan but would give illegal immigrants’ children a chance to achieve legal status.

Romney is on record saying he would veto the Democratic-sponsored Dream Act. “I would hope we could convince him to support a concept like this,” Rubio said at a forum hosted by National Journal on Thursday.

Romney’s campaign advisers reacted cautiously to Rubio’s efforts, saying the candidate will carefully study any such proposals. “We must work together on protecting and strengthening legal immigration, securing our borders, ending illegal immigration in a civil but resolute manner, and ensuring that any reforms do not encourage further illegal immigration,” spokeswoman Andrea Saul said in a statement.

Rubio’s efforts could put Romney in a political bind by forcing him to back away from his stated opposition to giving any legal status to those covered by the bill — or Rubio might be throwing him a political lifeline in a competition for voters destined to play a critical role in November and beyond.

Balz reported from Washington.