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Sen. Cochran is a conservative champion for American free enterprise, and his 88 percent lifetime record with the U.S. Chamber demonstrates his support for issues that will grow the economy and create jobs,” said Rob Engstrom, the chamber’s senior vice president and national political director. “The chamber is proud to stand with him.”

The chamber also is backing Mr. McConnell and Mr. Roberts in their re-election fights against Mr. Bevin, a Louisville businessman, and Mr. Wolf, a radiologist in the Kansas City area.

Both veteran lawmakers have benefited from their rivals’ rookie mistakes.

Mr. Bevin struggled to explain away his apparent support of the 2008 Wall Street bailout, an issue he has used to attack Mr. McConnell.

After bruising questions about how much time Mr. Roberts spends in Kansas, Mr. Wolf turned the focus of the race by posting patient X-rays to Facebook and then making off-color jokes about them.

“I don’t see Wolf honestly right now as a very serious challenger,” said Burdett A. “Bird” Loomis, a political science professor at the University of Kansas. “Milton Wolf had no political base at all in the state and every Republican virtually is supporting Roberts.

“I just have a very, very hard time compared to some other states as seeing this as serious,” he said. “If I was grading him on a 10-point scale, he’d maybe be a 2.5.”

Matt Hickam, a Kansas GOP strategist, said Mr. Roberts is working to make sure Mr. Wolf does not gain any momentum. The senator’s campaign is funneling more than $100,000 into an early television ad that says, “Wolf exposed private patient X-rays and other personal information on Facebook — where Wolf relentlessly poked fun at the dead or wounded.”

Pat Roberts is a Marine — he takes his battles very seriously,” Mr. Hickam said, adding that this is not the way Mr. Wolf wants to introduce himself to Kansas voters. “With this many missteps right out of the gate, it is going to be very difficult for him to recover.”