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Eric Cantor announced Wednesday he will step down as House majority leader on July 31 after suffering a stunning primary loss, touching off a leadership scramble at the top tiers of the Republican Party.

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Fox News is told a new leadership election will be held June 19, a little more than a week from now. Cantor, who said he will serve out the remainder of his seventh term as a Virginia congressman, told reporters he made the decision to give up his majority leader post with "great humility."

While he won't be on the ballot in November, he said, "I will be a champion for conservatives across the nation."

Cantor threw his support behind House GOP Whip Kevin McCarthy for the post, offering his "full support" and saying "he'd make an outstanding majority leader."

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    He stressed that he's not sure whether McCarthy is running, though he is widely expected to enter the competition. Reps. Jeb Hensarling, R-Texas, and Pete Sessions, R-Texas, are also considered potential candidates for the post.

    Cantor lost Tuesday night to Tea Party-backed rival Dave Brat, a little-known economics professor who stunned the political establishment. Asked Wednesday why he lost, Cantor responded: "I just came up short."

    He addressed reporters after a closed meeting with Republican colleagues. One lawmaker told Fox News that meeting was "emotional." In the meeting, according to sources, House Speaker John Boehner called for "unity."

    Cantor, too, urged colleagues to put "minor differences aside" and concentrate on the midterms. "What divides Republicans pales in comparison to what divides us as conservatives from the left and their Democratic Party."

    His departure, though, will trigger a heated set of negotiations between now and June 19.

    Several House members already were jockeying for position, making phone calls and lining up for the expected leadership race. If McCarthy runs and wins, his post would also be open, as would potentially others.

    "Members are freaking out right now," one senior House GOP source told Fox News earlier Wednesday, noting that nothing "rattles" lawmakers more than phone calls about who might support whom.

    One senior House GOP leadership aide said they need to have "direction."

    "It can't just be Lord of the Flies," the aide said.

    McCarthy would be considered a front-runner among some lawmakers. "It's Kevin's to lose," one member said.

    But the names being thrown in the pool of potential candidates for various positions were growing by the hour.

    GOP sources said Rep. Steve Scalise, R-La., head of the conservative Republican Study Committee, is interested in the position of Republican whip, as is Chief Deputy Whip Pete Roskam, R-Ill., if McCarthy leaves that post.

    Another aide said House Republican Conference Vice Chairwoman, Lynn Jenkins, R-Kan., a three-term lawmaker, would like to move up the leadership ladder "if an opportunity presents itself."

    Rep. Cathy McMorris Rodgers, R-Wash., the House GOP conference chairwoman, was apparently weighing the idea of running for whip or Cantor's job, but announced Wednesday she would stay in her current post.

    Cantor's loss was an unprecedented primary defeat for a sitting majority leader, and sets up the first leadership election in the middle of a congressional session since early 2006.

    That's when now-House Speaker John Boehner succeeded former House Majority Leader Tom DeLay, who stepped down from his post in 2005 after being indicted.
    Formal leadership elections are typically held in November, a few weeks after the general election. In the last "special" leadership election, Boehner won in an upset over then-Rep. Roy Blunt.

    In his press conference on Wednesday, Cantor also addressed speculation that his defeat could spell doom for immigration legislation, as his opponent ran in large part on accusing Cantor of backing "amnesty."

    Cantor said he still believes "there should be and is common ground" on immigration.

    "My position on immigration has not changed," he said.

    Meanwhile, there is the question of what Boehner wants to do and whether he feels pressure to leave.

    "Boehner's not going anywhere," a senior House Republican source who asked not to be identified told Fox News.

    Some believe Cantor's departure only makes him stronger because there's no one to challenge him -- as Cantor was believed to be the heir apparent.

    "We need Boehner now more than ever," said one former House Republican said. "Can Boehner step up?"

    Fox News' Chad Pergram contributed to this report.