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Tom Rath, a New Hampshire GOP strategist and former adviser to Mitt Romney’s 2012 presidential campaign, said Mrs. Ayotte remains popular with the state’s law enforcement officials and that the senator has plenty of time to respond before she has to worry about re-election.

“Typically a candidate gets in trouble when they do something contrary to what they said they are going to do, and the vote Sen. Ayotte cast is very consistent with what her position has been,” Mr. Rath said. “So, I don’t think anything changes much in the way of poll numbers, certainly not any change that has any impact on 2016.”