By Russell Berman - 06/12/14 08:45 PM EDT
Rep. Pete Sessions (R-Texas) ended his bid to become the next House majority leader on Thursday night, leaving Majority Whip Kevin McCarthy (R-Calif.) as the only candidate to replace Rep. Eric CantorEric CantorThe Trail 2016: On the fringe Cantor 'pleased' Trump is embracing Jeb Bush's immigration plan Trump’s Breitbart hire sends tremors through Capitol Hill MORE (R-Va.), who was defeated in a historic primary loss on Tuesday.
"After thoughtful consideration and discussion with my colleagues, I have made the decision to not continue my run for House majority leader," Sessions said in a statement.
Sessions is the House Rules Committee chairman and former head of the House GOP campaign committee.
Barring a late, new challenger, McCarthy will become the second-ranking House Republican after the leadership election scheduled for June 19.
While Sessions began seeking support within minutes of Cantor's surprise loss, he could not overcome the advantage that McCarthy had built up as the party's chief vote counter and top fund-raiser.
He also struggled to unify the conference's right flank. Many conservatives wanted another Texan, Rep. Jeb Hensarling, to seek the post, but he decided Thursday morning to stay out of the race. And as the Texas delegation deliberated over which member to support, McCarthy moved aggressively behind the scenes to lock down support.
McCarthy was further aided by Speaker John Boehner's (Ohio) decision to schedule the secret ballot election just over a week after Cantor's announcement that he would step down. The quick turnaround left little time for Sessions or other challengers to build enough support to take out McCarthy. Cantor will stay on as majority leader until July 31 to provide a transition.
Three other top conservatives, Reps. Paul Ryan (Wis.), Tom Price (Ga.) and Jim Jordan (Ohio), have also passed on the race.
Rep. Raúl Labrador (R-Idaho) is taking a look at challenging McCarthy, and a source familiar with his thinking said he's "getting a lot of encouragement from members." The conservative is well regarded by his fellow members of the 2010 GOP class, but it's not clear whether he could seriously threaten McCarthy.
With McCarthy likely to become majority leader, the more competitive leadership election became the race to replace him as whip.
That race pits McCarthy's chief deputy, Rep. Peter Roskam (Ill.), against the chairman of the conservative Republican Study Committee, Rep. Steve Scalise (La.), and another conservative, Rep. Marlin Stutzman (Ind.), who surprised many members with his entry on Thursday morning.
— This story was updated at 9:39 p.m.