The party’s top super PAC for House candidates said it had raised more this summer than ever before in a third quarter, but acknowledged the challenges Republicans are facing.

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Two major Republican super PACs are said to be withdrawing cash from the races of the incumbent Representatives Thomas H. Kean Jr. of New Jersey and Mariannette Miller-Meeks of Iowa in an effort to triage the midterm map.

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Howard Lutnick, the commerce secretary, made the donation after agreeing to an interview with lawmakers about his relationship with Jeffrey Epstein.

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