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Nevertheless, the poll said, he lost in a hypothetical matchup against former Secretary of State Hillary Rodham Clinton, a powerhouse with women and the consensus front-runner for the Democratic presidential nomination in 2016.

It was a more of an uphill battle for Mr. Cuccinelli in Virginia, where Mr. McAuliffe held a double-digit edge among women in the preliminary exit polls.

Former Rep. Thomas M. Davis III, Virginia Republican, said Mr. Cuccinelli suffered from sponsoring some “goofy bills” while in the state legislature.

“They are both pro-life. It is a question of how you present it,” Mr. Davis said about Mr. Cuccinelli and Mr. Christie. “You don’t have to be pro-choice to win statewide in New Jersey and Virginia, but you have to handle the issue appropriately. When you get into birth control and other issues like that, it gets more problematic. Christie didn’t do that.”