With Congress returning to Washington, D.C., from a week-long recess as lawmakers eagerly wait to see whether Rep. Paul Ryan makes a bid to become the next speaker of the House, all eyes will be on the House Freedom Caucus, the somewhat secretive group of far-right Republicans who in the past year have time and again been a thorn in their leadership’s side.

The caucus played a key role in toppling outgoing House Speaker John Boehner and helped derail House Majority Leader Kevin McCarthy’s bid for the top job. Now the big question is whether the group of approximately 40 Republicans – a small but powerful minority of the 246 GOPers in the House – would back Ryan, who is now open to running for speaker on the condition that he doesn’t have to negotiate with the Freedom Caucus for the position, according to NBC News.

That could be difficult.

Rep. Jim Jordan, chairman of the HFC, told MSNBC in an email that when it comes to selecting a new House speaker, any candidate would “need to demonstrate that he or she would allow good ideas to flow from the bottom up. Conference rules need to be reformed to empower the membership.”

The House Republican Conference is scheduled to meet at 7 p.m. ET Tuesday, then again at 9 a.m. ET the following morning.

There are also questions over whether the hard-line caucus would let Ryan off the hook for his more moderate stances on immigration and TARP, the Wall Street bailout program. The HFC’s support is seen as critical for any future speaker. After all, the caucus has enough members not only to block Ryan, but also any Republican-led legislation, forcing House leadership to go across the aisle for Democratic support.

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The HFC is relatively new, formed in January by nine congressmen with the mission of promoting “limited government, the Constitution, and the rule of law, and policies that promote liberty, safety and prosperity for all Americans.” Unlike other caucuses on Capitol Hill, there is no official roster. But the HFC clearly includes a number of lawmakers who rose to prominence during the 2010 Tea Party wave. Reuters describes the group as wealthier than their colleagues, in addition to being “overwhelmingly white, middle-aged and male.”

The caucus has plenty of critics who argue it isn’t interested in finding solutions but instead throwing verbal bombs and building procedural obstacles — which could have the unintended consequence of giving power to House Democrats by further dividing the GOP caucus. Boehner himself has referred to the HFC members as “knuckleheads.” Others have called them a “brat pack” and a secretive “Fight Club.”

“It’s a group of members who are engaged more in a game, a political game, and have more contempt for government than anything else,” said Thomas Mann, a congressional scholar and senior fellow of governance studies at Brookings Institution. “They are effective in destroying things but not effective in achieving anything.”

Rep. Jordan brushed off the criticism, calling it “spin from folks who want to make conservatives their scapegoat for not doing what voters sent them here to do. Our voters expect us to use the means at our disposal to make the argument for conservative principles, but instead we have too often done nothing until the last minute and then ceded the field to President Obama without a fight.” The HFC has previously argued against existing rules, insisting that bills are allowed on the House floor at the last minute without amendments. They also argue GOPers who don’t agree with the establishment can be booted from committees.

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What, if anything, the HFC has accomplished in the past year is a mixed bag. The most high-profile cases have been Boehner calling it quits and McCarthy dropping his House speakership bid. And indeed, Rep. Justin Amash, one of the caucus’ founding members, told MSNBC in an email that its biggest success “has been bringing attention to the speaker’s disrespect and disregard of the House rules and how this dysfunctional system has harmed our institution.”

In September, the HFC said its members would oppose any spending measure that continues funding for Planned Parenthood. Congress, however, managed to pass a short term spending bill to keep the government open through Dec. 11 without the policy rider.

The group also tried and failed to kill Obama’s Iran deal (a disapproval resolution failed to come to a vote in the House), opposed the Export-Import Bank, which expired, and has backed legislation banning the government from punishing churches or charities if they are against gay marriage.

But perhaps the biggest influence the HFC has had is that several lawmakers, as a result of the group, are now skeptical about wanting the speaker’s job at all – because spending the next year feuding with the caucus’ hard-line conservatives must sound like a nightmare.

“I think Ryan would be nuts to take the job because he’ll probably find himself in a position where he has to take actions to compromise, which will lead them to withdraw their support … It’s a dilemma that’s going to continue as long as the Freedom Caucus exists,” said Mann. The solution? “Drive them out of the party if you want to succeed in being a governing party. Otherwise the farce and chaos will continue indefinitely.”