The unexpected defeat of U.S. House Majority Leader Eric Cantor in a Virginia primary this week created a vacancy for his No. 2 job in the House Republican hierarchy, but the fight for the No. 3 job of majority whip is shaping up as the hottest post-Cantor battle — and Congressman Steve Scalise, of Jefferson, has emerged as a front-runner.

The current majority whip, Kevin McCarthy, of California, is regarded as the overwhelming favorite to succeed Cantor, who announced the day after his Tuesday primary loss that he would step down from his leadership post on July 31. In the game of leadership musical chairs, McCarthy’s move up would create an opening at whip.

Scalise, who has served in the U.S. House since 2008, and Deputy Whip Peter Roskam, of Illinois, first elected in 2006, stepped forward Wednesday as whip candidates. A third contender surfaced Thursday: Marlin Stutzman, of Indiana, who came to Congress in 2008.

There are no ribbon-cuttings at supermarket openings in the whip campaign, no kissing babies or TV attack ads. The constituency is small: the 233 members of the House Republican majority, who will fill the leadership vacancies in a closed-door meeting June 19. It takes a majority of the members present and voting to win, which could mean multiple ballots, if no one crosses the mark on the first round.

Campaigning for whip means contacting members to see where they stand, firming up commitments and trying to win over the undecided. Candidates rely on their “whip teams,” other members close to them, to do much of the leg work.

Scalise, 48, is chairman of the Republican Study Conference. The RSC is an adamantly conservative coalition that includes most of the House’s Republican majority. That provides him with a solid base from which to challenge for the whip position, although he has drawn some criticism in his 18 months as head of the group.

Scalise must have known he could count on U.S. Rep. John Fleming, of Minden: They share a state and a deeply conservative political philosophy, and Fleming, a physician, is an RSC member who helped draft the RSC alternative to Obamacare. Besides, he said Thursday that Scalise had sounded him out earlier — before the Cantor primary upset — as part of the groundwork for a potential future campaign for whip, should other potential election-related changes in the leadership provide an opening.

But just to be sure, Fleming said, Scalise’s chief of staff contacted her counterpart in Fleming’s office Thursday morning to make sure Fleming hasn’t changed his mind. He hasn’t, and he assured Scalise of that.

“I texted him back and let him know I was supporting him,” Fleming said.

Not only do they have much in common, but Fleming said he thinks Scalise has the people skills the job requires.

“He’s remained in warm relationships with people who are not as ideologically conservative as we are,” Fleming said.

Fleming thinks the ideology will work to his advantage against Roskam, who — although an RSC member himself — would generally be regarded as less conservative than Scalise. Stutzman, also an RSC member, muddies the ideological waters a bit, as he also leans to the right side of the Republican spectrum.

“There’s been a lot of discussion among conservative representatives, especially from the South, about wanting to have more representation in the leadership,” Fleming said.

That leadership has not changed since Fleming’s election in 2008, although the Republican caucus in the U.S. House has shifted rightward since then, most dramatically after the 2010 election sent a sizable cadre of tea party sympathizers to Congress. Some red-state Republicans have grumbled that the entire GOP House leadership is made up of representatives from states that Democrat Barack Obama won in both his presidential elections. Roskam, who was appointed deputy whip by McCarthy and comes from the president’s home state, wouldn’t change that; Scalise, from a state that twice rejected Obama, would; Stutzman falls somewhere in between: Obama won Indiana in 2008 but lost it in 2012.

Follow Gregory Roberts of The Advocate Washington bureau on Twitter, @GregRobertsDC