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No surprise there, said Mark Krikorian, executive director of the Center for Immigration Studies.

“The Democrats have successfully turned him into a hate figure, so it made sense when she picked him that they were going to use it against her,” Mr. Krikorian said. “The irony is that Pete Wilson is a moderate. He isn’t a restrictionist by any stretch of the imagination.”

He added that cutting off most benefits to illegal immigrants remains popular in California and elsewhere. Ten states have passed laws restricting benefits to illegal immigrants since Proposition 187, according to the Poizner campaign.

“Proposition 187 would probably pass again if they put it on the ballot, especially if they took out the education component,” Mr. Krikorian said. “So I’m not really sure Pete Wilson is the lightning rod for primary voters that the Democrat elites think he is.”