In the House, in addition to Mr. Sessions, leaders being challenged from the right include Eric Cantor of Virginia, the majority leader, and Representative Greg Walden of Oregon, chairman of the National Republican Congressional Committee. In all, six Republican committee chairmen in the House face contested primaries, including Fred Upton of Michigan, of the Energy and Commerce Committee, and Frank D. Lucas of Oklahoma, of the Agriculture Committee.

In the Senate, the No. 1 and No. 2 Republicans are fighting off Tea Party-inspired challengers. Mitch McConnell of Kentucky, the minority leader, will square off in May against Matt Bevin, a Louisville businessman who has endorsements from activist groups like Senate Conservatives Fund and FreedomWorks. In Texas, John Cornyn, the minority whip, faces a seven-way primary. One of his opponents is another member of the Texas congressional delegation, Representative Steve Stockman.

With little interest in coming to Congress to build bridges, these candidates often invoke Senator Ted Cruz of Texas as their model. Given what happened this month when Mr. Cruz used a filibuster threat to back Mr. McConnell and Mr. Cornyn into a corner over the vote to raise the debt ceiling, many Republicans seem less than enthusiastic about a 2015 freshman class full of Cruz acolytes.

“We’ve seen this movie before,” said Senator Bob Corker of Tennessee, one of the Republicans who said that these efforts are often stunts to raise money and build national profiles. “People can raise lots of money in those shows if that’s what their intentions are.” (Many of the “Fire the Speaker” online petitions, in fact, have large “donate” buttons at the bottom of the page, with the proceeds going to groups like FreedomWorks and Tea Party Patriots.)

These politicians, many of them in their 30s and 40s, take a less deferential view toward their party leaders, revealing how divisions among Republicans have become ideological as well as generational.