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Like many candidates attacked over budgets, Thom Tillis, a Republican running for the Senate from North Carolina, responded in a recent debate by disputing his opponent’s numbers.

“Kay’s math just doesn’t add up,” he said. The Democratic incumbent, Senator Kay Hagan, seized on that small opening to claim personal offense. “I’m actually insulted,” she declared. “I understand math.”

The Democratic Senatorial Campaign Committee, counting heavily on women to turn out across the country, accused Mr. Tillis of “mansplaining” and “condescension” toward his female adversary. On anyone’s outrage meter, it was tame stuff compared with the incendiary comments about rape that hurt Republican candidates so badly two years ago.

But Democrats must wage “war on women” attacks against the opponents they have, not the ones they wish they had. The dearth of such ammunition this year is no accident. Republican strategists in Washington have worked to smother the most ideologically extreme candidacies and have girded themselves for attempts to cast the party as hostile to women.

“We’ve been preparing for this,” said Sara Fagen, a former aide to President George W. Bush. This week’s New York Times/CBS News poll brought her party encouraging news: Men said they planned to vote Republican by a double-digit margin, while Democrats’ one-point lead among women fell well within the poll’s margin of sampling error.

The longstanding partisan split between men and women is driven by divergent views over the role of the government, and on social programs, military spending, health care and other issues. Those disagreements will play the biggest role in this fall’s fight for control of the Senate.

But campaign operatives forage incessantly for material to stoke outrage, generating campaign cash and fueling turnout. In 2012, Democrats trumpeted Mitt Romney’s surreptitiously recorded “47 percent” remarks as proof that he scorned Americans receiving government assistance; Republicans exploited President Obama’s “you didn’t build that” riff to call him hostile to business.

In the struggle for female voters, 2012 Republican Senate candidates set the gold standard for outrage. Todd Akin of Missouri cast doubt on the occurrence of pregnancy in “a legitimate rape,” explaining that “the female body has ways to try to shut that whole thing down.” Richard Mourdock of Indiana later called pregnancy resulting from rape “something that God intended to happen.”