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Mr. Christie, though, has some challenges to overcome as the polling shows that he is the most polarizing figure among the crowded field of likely GOP contenders.

“He is leading right now if you ask people who they are going to vote for, but he is also leading in the dubious honor of which candidate you would not vote for under any circumstances,” Mr. Smith said.

“The reason for that does not necessarily have anything to do with Bridgegate. I think it is because he is not seen as the conservative candidate at a time when the conservative wing of the political party is the one that has the political energy and political juice right now.”

The discontent with Mr. Christie was laid bare on Wednesday when the Judicial Crisis Network, a conservative group, began airing television, radio and digital ads calling into question his record on judicial nominations and criticizing him for not pushing the New Jersey Supreme Court in a more conservative direction.

Chris Christie promised to change New Jersey’s liberal Supreme Court. Over and over he broke his promise. The court remains liberal. Call Chris Christie,” the narrator says in the commercial. “Tell him to fight for judges who respect the rule of law,” continues the narrator.

Earlier this month, the group welcomed Mr. Christie to Iowa with similar ads, warning that he sided too often with New Jersey’s Democratic-controlled legislature, including in May, when the two sides struck a deal in which Mr. Christie agreed to nominate Chief Justice Stuart Rabner, a Democrat, for tenure.

Mr. Rabner angered conservatives in 2013 when he wrote the opinion that legalized same-sex marriage in New Jersey and refused to put a stay on the ruling.