Rep. Jeb Hensarling (R-Tex.), chairman of the House Finance Services Committee, will not run for House majority leader, according to three people familiar with his plans.

The congressman was a no-show Thursday morning at a secret meeting of about 40 conservatives, mostly from Southern states, held on Capitol Hill.

Hensarling was considered the best chance for some of the House's most conservative members to elevate a colleague into the leadership ranks. Since the stunning loss of House Majority Leader Eric I. Cantor in the Virginia GOP primary Tuesday night, Hensarling had consulted with colleagues, including House Budget Committee Chairman Paul Ryan (R-Wis.) and Rep. Tom Price (R-Ga.), a key conservative broker and member of the Republican Study Committee.

Hensarling's decision leaves Rep. Pete Sessions (R-Tex.), chairman of the powerful House Rules Committee, as the only likely opponent against House Majority Whip Kevin McCarthy (R-Calif.), who has sought to quickly shore up support to take the leadership spot after Cantor steps down July 31.

Using his deep network of supporters, deputy whips and a paper-based scoring system that dates back to the House leadership races of the 1990s, McCarthy and his team were asserting momentum Wednesday night as Hensarling was still mulling whether to join the fray.

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