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But Mr. Boisture said he’s not enthusiastic about sending Mr. Murphy to the Senate either, saying the three-term congressman “hasn’t done so well” in Congress.

“We’re sitting here in Connecticut with one of the highest unemployment rates of anywhere in the country,” Mr. Boisture said. “I think people are just saying you know what, it almost doesn’t matter where she came from. We just need somebody different.”

Besides just deflecting attention away from the WWE and onto Mr. Murphy, voters say they’ve seen Mrs. McMahon soften her image, playing up her roles as a wife and mother and especially courting the female vote.

“She has run a very savvy advertising campaign, which for the most part has recharacterized her as being a mother, kind, that sort of thing, as opposed to the wrestling,” said Groton resident Tim Bates, who said he’ll nonetheless be voting for Mr. Murphy.