The manufacturing executives had gathered in an Atlanta conference room last year to honor their senior United States senator, Johnny Isakson, for his tireless efforts on their behalf in Washington. But as the luncheon wound down, Mr. Isakson found himself facing a man from Coweta County. The man, Burl Finkelstein, said trade policies with Mexico and China were strangling the family-owned kitchen-parts company he helped manage, and imperiling the jobs it provided. Mr. Isakson politely brushed him off, Mr. Finkelstein recalled, as he had many times before. So when the Georgia primary rolled around this month, Mr. Finkelstein, along with...