Update: The Post's Robert Costa and Ed O'Keefe report that Hensarling won't run.

It didn't take long for the race to succeed House Majority Leader Eric Cantor (R-Va.)  as the second-ranking House Republican to ramp up. Behind the scenes, would-be contenders are making calls, measuring support and plotting their futures. With the election set for June 19, there isn't much time for campaigning.

Here's a look at the names that have emerged as he strongest possibilities:

House Majority Whip Kevin McCarthy (Calif.)

House Majority Whip Rep. Kevin McCarthy (R-Calif.), center (Alex Wong/Getty Images)

What's his deal? McCarthy is currently the third-ranking House Republican. He has risen through the ranks swiftly. First elected in 2006, McCarthy chaired the Republican Platform Committee in 2008. Along with Reps. Paul Ryan (R-Wis.) and Cantor, he started the GOP's now well-known "Young Guns" candidate recruitment program.

Why he'd win: Three reasons. First, speed. As The Post's Robert Costa and Ed O'Keefe reported, McCarthy was moving swiftly Wednesday to gauge support and had already deployed a numerical ranking system that assigned his colleagues numbers based on how likely they are to support him. “1” means the memebrs is a loyalist, while a “5” denotes a someone who needs more convincing. Second, McCarthy is a strong fundraiser and well-respected by both the establishment wing of the GOP Conference. Three, politics is often hierarchical. And McCarthy is next in line.

Why he wouldn't: Conservative angst. Erick Erickson, a well-known conservative blogger, wrote Wednesday that "McCarthy is not very conservative and, for all of Cantor’s faults, lacks Cantor’s intelligence on a number of issues. Lest we forget, McCarthy had several high profile screw ups as Whip and has not really seemed to ever improve over time." Mark Levin, the conservative radio host who backed Cantor's primary opponent also knocked McCarthy.

Rep. Jeb Hensarling (Tex.)

House Financial Services Committee Chairman Jeb Hensarling (R-Tex.). (Gary Cameron/Reuters)

What's his deal? He was first elected in 2002 and has served in leading roles in the House. He used to be the House GOP Conference Chair and currently heads up the Financial Service Committees.

Why he'd win: If Cantor's primary loss creates a sweeping sense in the House GOP Conference that leadership needs a shake-up, then he will have a chance. Conservative leaders outside Congress like Erickson have talked him up, while in the House, conservative Reps. Jim Jordan (R-Ohio) and Rep. Justin Amash (R-Mich.) have giving him their blessing. Plus, he is from Texas, a state whose delegation that makes up a sizable chunk of the GOP Conference.

Why he wouldn't: For one thing, it's not 100 percent clear he will run. Costa and O'Keefe reported that he was playing his cards close Wednesday. Even if he does, McCarthy would be an imposing competitor who would not be an easy out.

Rep. Pete Sessions (Tex.)

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

What's his deal? Sessions is a former chairman of the National Republican Congressional Committee, the campaign arm of the House GOP. First elected in 1996, Sessions has been in the House the longest of the three names on the short list.

Why he'd win: He heads the powerful House Rules Committee. And power is a good way to win allies. He oversaw the NRCC during the 2010 cycle, a GOP wave year in which many of the House GOP's newest members were elected. He sounds confident, predicting to Costa that he would beat McCarthy.

Why he wouldn't: If both Sessions and Hensarling run, it could divide the Texas delegation, which would work to McCarthy's advantage. Not only that, but if Sessions runs as the more conservative alternative to McCarthy and Hensarling is also in the race, support on the right could also be split.


Here are six prominent Republicans to watch in the House leadership upheaval after Rep. Eric Cantor's primary loss and resignation as majority leader. (Theresa Poulson/The Washington Post)