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Last week, he sparked attacks from Democrats after he said he would veto the Dream Act, which would legalize some illegal immigrant students and young adults. Those illegal immigrants, often brought to the U.S. as infants, are considered among the most sympathetic of candidates for legal status.

Asked if there was any room for exceptions, Mr. Romney said he might allow some hardship cases, but left little wiggle room beyond those already built into current law for refugee cases or Cuban immigrants.

“The comment ‘no circumstances’ is a very broad term, and so if you’d like us to go into specific examples, for instance, a child that’s a refugee, a child that comes from a politically unstable place, uh, Cuba,” he said. “So there are many different circumstances I would have to consider.”

He said in formulating his broader immigration policy, he will continue to push for a system that does not give illegal immigrants an advantage.

“I will put out a series of immigration proposals before November of 2012, and I will look at adjustments to the law that I think may be necessary, but my principle is straightforward, and that is that those who come here illegally really should not be given a preferential path to permanent residency or citizenship,” he said.