The race to succeed Rep. Eric Cantor as House Majority Leader began Wednesday morning, just hours after the Virginia Republican was ousted in a GOP primary in stunning fashion.

House Majority Whip Kevin McCarthy of California and House Rules Committee Chairman Pete Sessions of Texas, two fierce rivals within the senior GOP leadership ranks, began courting members almost immediately upon Cantor's loss to upstart challenger Dave Brat, a college economics professor.

Sessions was chairman of the National Republican Congressional Committee in 2010, when the GOP won its biggest majority since World War II.

Sources told the Washington Examiner that his pitch to members would be that he is the more conservative of the two candidates, but that he also is a proven fundraiser who knows how to run the floor.

Sessions is likely to remind members that in 2004, he was one of the few congressional Republicans who crossed the Bush administration and other party leaders and endorsed Pat Toomey in his GOP primary challenge of Sen. Arlen Specter.

McCarthy, the No. 3 ranking Republican, has better relationships with members and has been more active recently in helping them raise money and move legislation, is viewed as the early favorite in a head to head against Sessions. McCarthy helped recruit many of the members who were elected in 2010 and is a fundraising powerhouse in his own right. The looming question is whether a third heavyweight candidate joins the race.

House Financial Services Chairman Jeb Hensarling of Texas, already favored by House conservatives to challenge House Speaker John Boehner of Ohio for the gavel, could run, although he had been disinclined to seek a senior leadership post this year -- at least before Cantor lost. Of note, Sessions and Hensarling both hail from Dallas; Sessions used to represent portions of Hensarling's congressional district. Hensarling was Sessions' finance chairman at the NRCC in 2010.

“Jeb did not come to Congress with the intention of becoming a member of leadership,” one Republican source said.

Republican sources, including members, said they expected Cantor to step down as majority leader within days if for no other reason that he cannot perform the duties of his leadership post as a lame duck. As the No. 2 ranking member of the House majority, Cantor is responsible for setting the legislative agenda and raising campaign cash for House campaigns.

With the midterm elections around the corner, Republicans said they need an individual in place who can do those jobs -- and immediately.

“He has to step down,” one Republican member told the Washington Examiner. Although this was not necessarily the consensus view among members and congressional aides, it was an opinion that was picking up steam. Tuesday evening, in the immediate aftermath of Cantor’s loss, many thought he could stay on the job.

“Typically the majority leader raises money and makes campaign appearances in tight races. Cantor cannot perform that service,” a veteran GOP lobbyist said.

Added a GOP operative: “Getting a new unified leadership team in place now, rather than six months of palace intrigue is probably best for the long term, but Eric's earned the right to make that decision for himself.”