WASHINGTON — As Speaker John A. Boehner set leadership elections for the House of Representatives next week, the top candidate to replace him found himself under a harsh glare for comments he made suggesting that Hillary Rodham Clinton’s poll numbers were dropping in part because of a Republican-led inquiry by the Select Committee on Benghazi.  In an interview with Sean Hannity of Fox News, Representative Kevin McCarthy, the Republican majority leader who wants to succeed Mr. Boehner, said: “Everybody thought Hillary Clinton was unbeatable, right? But we put together a Benghazi special committee, a select committee. What are her numbers today? Her numbers are dropping. Why? Because she’s untrustable.”  Mr. McCarthy added, “But no one would have known any of that had happened had we not fought and made that happen.”  His comments stoked an immediate feud with Democrats, who accused Republicans of politicizing the inquiry.  “This stunning concession from Representative McCarthy reveals the truth that Republicans never dared admit in public,” said Representative Elijah E. Cummings, the lead Democrat on the committee. “The core Republican goal in establishing the Benghazi Committee was always to damage Hillary Clinton’s presidential campaign and never to conduct an evenhanded search for the facts.”  A look at the advantages and disadvantages of potential candidates to replace House Speaker John A. Boehner.  Brian Fallon, a spokesman for Mrs. Clinton, called Mr. McCarthy’s remarks “a damning display of honesty by the possible next speaker of the House. Kevin McCarthy just confessed that the committee set up to look into the deaths of four brave Americans at Benghazi is a taxpayer-funded sham. This confirms Americans’ worst suspicions about what goes on in Washington.”  The remarks about the Benghazi investigation were not the only subject where Mr. McCarthy generated controversy. He also seemed critical of the man he seeks to replace, Mr. Boehner.  “I think John Boehner deserves a B-,” Mr. McCarthy said in the interview. Even though Mr. McCarthy is the second-ranking Republican in the House, he has repeatedly said the leadership team he helped anchor is not in touch with voters.  Mr. Boehner’s retirement has set off a series of contentious challenges to fill the leadership positions. House Republicans seeking those posts have been furiously lobbying fellow Republican colleagues for their support.  On Tuesday night, House Republicans met to air their grievances and to discuss a framework for a legislative strategy going forward, but no consensus emerged.  After a difficult few months of infighting, many members are eager to put a new leadership team in place and prepare for fiscal battles that await them in December.  “After consulting with our conference, a large majority of our members have made clear they want these elections held next week,” Mr. Boehner said. “With their considerations in mind, the House leadership elections will take place on Thursday, Oct. 8.”  In deciding to hold the elections so quickly, Mr. Boehner appeared eager to have the new leadership chosen before a Columbus Day congressional recess. Otherwise, the contest might have dragged on for nearly a month. Mr. Boehner had his own experience in 2006 with a drawn-out battle for majority leader against Roy Blunt of Missouri, and Republicans at the time vowed to prevent that from happening again.  The next speaker of the House will need 218 votes on the House floor, but once that election is held, Republicans will fill the next three slots — majority leader, majority whip and conference chairman — with only a majority of Republican votes required.
As the House prepared to choose new leaders, Mr. McCarthy tied the Republican-led Benghazi inquiry to Hillary Rodham Clinton’s dropping poll numbers.