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The latest polls show the two men running neck-and-neck in a state that went for Mr. Obama in 2008 after decades of backing Republican presidential candidates.

Mr. Romney’s reluctance to stake out a clear position on the recent immigration news represents a dramatic shift from the Republican primaries, when he emerged as the most ardent opponent of amnesty - vowing to veto a Democratic version of the Dream Act and using the issue against his Republican rivals.

When Texas Gov. Rick Perry emerged as his toughest competition, Mr. Romney attacked his decision to sign a bill granting in-state tuition to the children of illegal immigrants. He also pounced on former House Speaker Newt Gingrich after the former House speaker suggested he was open to granting some sort of legal status to many illegal immigrants with deep roots in the country.

“I’m not going to start drawing lines here about who gets to stay and who gets to go,” Mr. Romney said in a November debate. “The principle is that we’re not going to have an amnesty system that says that people who come here illegally get to stay for the rest of their life in this country legally.”

Ms. Navarro said that until he says otherwise, Mr. Romney could be boxed in by what he said during the Republican primary.

“He said some things during the primary which have put him in a difficult position, but there is still a lot of room for him to fill in the blanks and for him to try to climb out of that box,” she said. “The problem is that unless he says more on immigration, he is going to be judged by what he said during the primary.”