Rep. Pete Sessions (R-Tex.) (Melina Mara/The Washington Post)

The race to be the next House majority leader began to crystallize Thursday as one leading conservative announced that he will not seek the position, while another top contender was asserting that he had all the votes he needed to win.

But allies of Majority Whip Kevin McCarthy (R-Calif.) were claiming momentum Thursday morning in the race to succeed House Majority Leader Eric Cantor (R-Va.), hoping to swiftly seal the deal. That confidence came as Rep. Pete Sessions (R-Tex.), chairman of the House Rules Committee, vowed again Thursday morning to mount a serious campaign for the job.

Sessions did so after Rep. Jeb Hensarling (R-Tex.), chairman of the House Finance Services Committee, said Thursday morning that he wouldn’t run for leader — a blow to the most conservative Republicans who saw him as their best chance to elevate a like-minded colleague into leadership.

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