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And the U.S. Chamber of Commerce, the nation’s biggest business lobby, spent $600,000 opposing Jose Hernandez, a Democratic candidate in California, on top of “a $1.8 million commitment from the American Action Network,” campaign manager Dan Krupnick said.

In Mr. Hernandez’s corner was only the House Majority PAC, at $475,000 — plus, as if to highlight the relative scarcity of funds, a mere $10 from the Sierra Club.

“These people come in and throw bombs and they try to see what sticks,” Mr. Krupnick said.

In Ohio, where redistricting has brought a rare race between two incumbents, outside groups have spent well over twice what Reps. James B. Renacci, Republican, and Betty Sutton, Democrat, have spent, thanks largely to $1.3 million from the AFL-CIO and $500,000 from the Service Employees International Union.