After months of a bruising television ad war between Dr. Mehmet Oz and David McCormick and their allies, the relatively shoestring campaign of Kathy Barnette, a conservative commentator showing surprising strength in the polls, will receive a late boost in the Republican primary for Senate in Pennsylvania. The Club for Growth, the pro-business and anti-tax group, began booking television ads on Tuesday on behalf of Ms. Barnette worth $2 million, according to AdImpact, the ad-tracking firm. The new ad has Ms. Barnette narrating her impoverished upbringing on “a pig farm in Alabama” and saying how “this country allowed a little...