When the House broke for its August recess, Republican Rep. John Fleming went home to Louisiana to connect with voters. He got an earful.

He traveled the state, and whether he spoke with a lowly company employee, a middle manager, or a business owner, they all said the same thing: “They are very disappointed in how we Republicans are doing in Washington,” says Rep. Fleming, a physician elected in 2008.

Fleming says his constituents see a GOP-controlled Congress failing to check President Obama, even as federal regulations are hurting them personally. It doesn’t matter to them that the president has veto power, or that Democrats can still block Republicans in the GOP-controlled Senate.

“They just don’t want to hear that. That’s an excuse to them,” he says in an interview. “They at least want a fight.”

Fleming is doing his darndest.

In January, he and eight other hard-line Republicans formed the House Freedom Caucus to challenge the GOP leadership, which they claim is not fighting hard enough for Republican priorities. Now they’re bigger and they're emboldened. They just succeeded in driving out Speaker John Boehner (R) of Ohio, who recently stunned Washington with the news that he will retire from Congress on Oct. 30.

In the weeks ahead, the Freedom Caucus will have plentiful opportunities to push the fight further – from the speaker's race to a combustible mix of fiscal deadlines this fall. Though members say they have not yet settled on a strategy, one thing is certain: They are not afraid of government shutdowns, fiscal cliffs, or any other hardline tactics that typically made Boehner wince.

Republicans have not gotten what they wanted, they say, not because these gambits failed, but rather because leadership didn't commit to them, heart and soul.

And they want that to end now.

Turmoil is not the problem

For this invitation-only group of about 40 members, which meets regularly at a Capitol Hill restaurant called the Tortilla Coast, the fight starts with the GOP's election for the speakership and other GOP leadership offices, which will take place in a secret ballot on Thursday.

Mr. Boehner said he wanted to spare his members and the institution the “turmoil” of an expected attempt to oust him. But to many conservatives, like the members of the Freedom Caucus, turmoil is not the problem. They want real change in the top-down way the House is run and are making demands.

That pressure bubbled over Sunday when Rep. Jason Chaffetz (R) of Utah suddenly joined the race, challenging Boehner’s presumed successor, Rep. Kevin McCarthy (R) of California. Congressman Chaffetz says he was "recruited" as an alternative to majority leader McCarthy. He doubts Boehner’s right-hand man can get enough conservatives to win a final floor vote for speaker without having to rely on Democrats. That vote will occur at the end of the month.

"You don't just give an automatic promotion to the existing leadership team," Chaffetz said on "Fox News Sunday." Voters “want us to take that fight to the Senate. They want us to take that fight to the president.”

Beyond the race for the speakership, the House has a to-do list chock full of pressure points for the Freedom Caucus, including debt, budget, and tax deadlines. Many in Washington are quaking over the deadlines. They remember previous cliff-hanger negotiations between the Obama administration and Republicans in Congress. They wonder whether the Freedom Caucus will trigger a government shutdown over federal funding for Planned Parenthood, the way hardliners did over Obamacare in 2013.

Caucus members see the coming weeks as an opportunity. Exactly what their fight will look like “is kind of fluid,” says Rep. Matt Salmon (R) of Arizona, another caucus founder. But “as we go forward, we’re going to consider anything and everything,” he said last week.

Whether Republicans are fighting hard enough for their priorities is a matter of opinion, and forms a dividing line in the party that runs from voters, to Congress, to the presidential race.

Sixty percent of Republican voters say they feel “betrayed” by their political party, according to a September Fox News poll. Two-thirds of GOP primary voters do not believe Republican majorities have done enough to block Obama’s agenda, the poll finds.

The benefits of a shutdown

“It’s somewhat subjective, 'Did you fight hard enough for your priorities?' With Boehner, the answer is, ‘No, you didn’t,’ ” says Matt Kibbe, the former head of the tea party advocacy group Freedom Works.

Mr. Kibbe is the kind of person Boehner means when he rails against “false prophets” who gin up the base with unrealistic promises. The speaker blames outside groups such as Freedom Works and Heritage Action for egging on the 2013 shutdown, a strategy he says was doomed to fail. He and Senate majority leader Mitch McConnell (R) of Kentucky have since vowed not to repeat a shutdown.

But Kibbe says it is Boehner who is the false prophet, promising in the 2010 GOP “Pledge to America” to roll back spending to 2008 levels and to repeal Obamacare if the Republicans won the House.

“You have to believe that they never meant it,” says Kibbe, who is now a senior adviser to Concerned American Voters, a super political action committee for GOP presidential candidate and libertarian, Sen. Rand Paul of Kentucky.

“This idea that shutting down the government is a fundamental loser for Republicans – I just don’t buy it,” Kibbe continues. He notes that it was only after the shutdowns of 1995 and early ’96 that Republicans, under the leadership of Speaker Newt Gingrich, were able to strike a deal on welfare reform with President Clinton.

“Clinton took Gingrich seriously; Obama has never taken Boehner seriously.”

Fleming couldn’t agree more. He points to the stunning midterm election of 2014, which returned a historic number of Republicans to the House and handed the Senate to GOP control – despite the shutdown the year before.

Republicans rarely put a bill on the president’s desk that he doesn’t like, Fleming complains. Indeed, the president has only vetoed four bills in his seven years in office – though he’s made plenty of veto threats.

“We could be getting more than we’re getting now,” Fleming says. “By raising the white flag before the discussion debate even begins, we’ve already lost.”

Blackmailing your friends

Other Republicans – hardly moderates – don’t see it that way.

Take Grover Norquist, founder and president of Americans for Tax Reform. He’s famous for his Taxpayer Protection Pledge to oppose tax increases. Most Republicans in Congress have signed it.

Ideologically, Republicans are more united today than ever, he says. What Republican is for Obamacare? Or for tax increases?

Under Boehner’s leadership, he notes, the House scrapped earmarks. Republicans negotiated permanent tax cuts for most Americans. They got budget caps and the first real spending cuts since the end of World War II. They reformed a part of Medicare in what’s known as the “Doc Fix.” They even sued the president.

“People take progress for granted,” says Mr. Norquist. “What you would like is not the question. I would like rubies and diamonds.... It's, 'What can you accomplish?’ ”

In Congress, a backlash may be building against Freedom Caucus hardball tactics. Last month, a caucus member quit, saying tactics were harming, not helping, the GOP cause. Over in the Senate, Republican colleagues shouted down tea party favorite Sen. Ted Cruz (R) of Texas last week over his procedural move related to spending and Planned Parenthood.

“There’s a lot of frustration. In some sense, this group treats Republicans like they’re their enemy,” says Rep. Tom Cole (R) of Oklahoma, a Boehner supporter. “It’s always inappropriate to try and blackmail your teammates.”

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The Oklahoman understands the anger of Freedom Caucus members. The political roadblocks to the GOP agenda frustrate him, too, but anger clouds their judgment, he says. The caucus pursues things that “demonstrably don’t work,” such as threatening to shut down the Department of Homeland Security over the president’s immigration policy.

Cole hopes that a new speaker can help calm the waters. “I think we’ve got an opportunity for a little bit of a new beginning.”