House Majority Leader Eric Cantor's supporters believe he will have the votes to become the next speaker if John Boehner exits. He has cultivated relationships with members, raised $17 million for House campaigns and assembled an agenda aimed at appealing to 2014 voters.

But that doesn't mean he's a shoo-in for the post, many in Congress believe.

Several qualified candidates are sure to at least give serious thought to challenging Cantor.

"There very well might be competition," Rep. John Fleming, R-La., a Tea Party Republican, told the Washington Examiner. "Because it's an open seat, not because it's Eric Cantor."

Some GOP leadership aides, none of them willing to go on the record, say there will be a fight for the speakership in part because Cantor has angered some members of the party, particularly those who consider themselves aligned with the Tea Party.

One Republican lawmaker who won't be supporting Cantor recounted a conversation the two had recently on the House floor during a vote.

"He basically said, 'Yeah, I'll listen to you, but vote the way I tell you,' " the member recalled, adding, "That's not what my constituents expect me to do."

Some other Republicans who might vie for the speaker's gavel include:

– Rep. Paul Ryan, R-Wis.: The head of the House budget Committee fortified his role as a consensus builder by helping to pass the 2014 budget deal without a government shutdown. But Ryan has alienated some conservatives by restoring $63 billion in sequester cuts and by signaling support for comprehensive Immigration reform. Many lawmakers believe he's not interested in the speaker's job. Ryan recently told the Wall Street Journal he wants to take the helm of the powerful House Ways and Means committee.

Kevin McCarthy, R-Calif.: The House Majority Whip is the number three House GOP leader, well-liked by the rank and file and familiar to many lawmakers thanks to his role as chief arm-twister.

– Greg Walden, R-Ore.: Walden is head of the National Republican Congressional Committee, the fundraising and campaign arm of the House GOP, and admired by the rank and file for his listening skills. "He's built a lot of relationships with people," one leadership aide said.