The CNN/Time poll showed that Mr. Blumenthal owes his lead in the race to his support among women. While the race is tied among male voters, women favor him 61 percent to 34 percent. Over all, among likely voters, Mr. Blumenthal is backed by 54 percent, and Ms. McMahon is supported by 41 percent.

Men often praise Ms. McMahon’s business acumen and some show up at her campaign events, eager to talk to her about wrestling and to be photographed with her.

Ms. McMahon’s campaign is trying to soften her image to reach women. On the trail, she describes herself as a mother, grandmother and wife, and she addressed a recent appeal to “moms across Connecticut.”