In any hostage negotiation, there are demands.

Authorities aim to end them peacefully, but what happens when the captors don't want anything but to cause chaos?

Kevin McCarthy, in his long quest to become speaker, remains a handful of votes short, the GOP conference and the House itself remain paralyzed — and there's no SWAT team to swoop in and end the standoff.

The number has now grown to 21 members who declined to vote for McCarthy, as he's failed in six rounds of voting. It's the first time in 100 years that voting for a speaker has gone beyond one round, and those opposing McCarthy now hold the key.

To be elected speaker in this new Congress with just Republican votes, any Republican can only lose four votes. Because of how narrow Republicans' majority is after the midterm election results, a small cadre of intransigent members on the party's far right have a lot of leverage — and they're showing they're willing to use it.

What it boils down to for these members is three things:

wanting to see less government spending,

more power to them and less power for the speaker, and

mistrust and personality differences

It's not clear, though, if there's anything McCarthy can do to persuade them. Some have made clear they want further concessions from him. McCarthy backed the hard-right faction's proposal for a five-vote threshold to remove the speaker, but he wouldn't accept other demands, like putting more restrictions in place from members earmarking spending on unrelated bills for their own projects, or committing to bringing a bill to the floor to impose term limits.

Meanwhile, there are a handful of others who appear to be immovable.

The core of this group are anti-establishment, ideologic skeptics of government. They want it to be smaller, do less, to spend less and are hard line on immigration. Most were endorsed by former President Donald Trump, and many are election deniers, but even Trump's influence is only going so far in this fight.

So who are they and what, if anything, do they want?

Rep. Andy Biggs, R-Ariz.: Biggs is one of the leaders of this movement. He stepped forward to challenge McCarthy and was the first nominated by this hard-right opposition, winning votes on the first two ballots.

Rep. Dan Bishop, R-N.C.: The House Freedom Caucus member was one of seven members to sign a "Dear Colleague" letter outlining concerns, like "increasingly centralized decision-making power" that result in "massive, multi-subject bills that are unable to be amended or fully read, all driven by supposedly must-pass defense and appropriations measures" that amass large debt.

(The other six to sign the letter were: Republican Reps. Scott Perry of Pennsylvania; Paul Gosar of Arizona, Andy Ogles of Tennessee, Chip Roy of Texas, Andrew Clyde of Georgia and Eli Crane of Arizona.)

Rep. Lauren Boebert, R-Colo.: The controversial Colorado firebrand narrowly won reelection by only hundreds of votes. She and others want a single member to be able to bring a motion to vacate the speaker.

Josh Brecheen, R-Okla.: The rancher and construction company owner is a new member of Congress, who aligned himself with the House Freedom Caucus during his campaign.

Michael Cloud, R-Texas: Cloud cites wanting to get the country on a "path toward fiscal responsibility" and notes that he'd "worked for months in high hopes and good faith that our conference would chart a course away from the status quo."

Andrew Clyde, R-Ga.: The gun shop owner, who sent an encouraging text about Trump to White House Chief of Staff Mark Meadows days after Jan. 6 and previously called McCarthy "a friend," was one of the seven signers of the December "Dear Colleague" letter that outlined fiscal issues and large spending bills as a major problem.

Eli Crane, R-Ariz.: The Trump-backed freshman, who flipped a House seat in November, was also one of seven signers.

Byron Donalds, R-Fla.: Donalds' opposition was a particularly worrisome sign for McCarthy. Though he is a member of the conservative Freedom Caucus, he was willing to initially vote for McCarthy, which he did on the first two ballots. He became the unlikely landing place for the 20 votes, himself winning those opposition votes on the last few ballots. He says he switched because McCarthy "doesn't have the votes," that negotiations need to happen.

Matt Gaetz, R-Fla.: Gaetz has been a principal instigator and steadfast opponent of McCarthy in this process. "Maybe the right person for the job of speaker of the House isn't someone who has sold shares of themself for more than a decade to get it," Gaetz said Tuesday.

Bob Good, R-Va.: Good, who has been at the forefront of the opposition, seems like one of the most dug in members. Good calls McCarthy part of the "swamp cartel," claims that despite giving McCarthy a chance over the last couple of years, he hasn't done enough to stop massive spending bills and hasn't fought hard enough against the "Biden-Schumer agenda." He's also been critical of McCarthy's PAC spending money, he says, against conservatives. McCarthy's PAC said Wednesday night that it promised not to play in open primaries where there is no incumbent.

Paul Gosar, R-Ariz.: Gosar is one of the most controversial members of Congress. He's defended white nationalists and spoken to them and was censured after posting an anime video depicting the killing of Democratic Rep. Alexandria Ocasio-Cortez and President Biden. He's also one of the leaders of this insurrection against McCarthy and was the first to rise to nominate an alternative. Gosar went viral Tuesday when he was spotted having a conversation with Ocasio-Cortez on the House floor about whether Democrats would help McCarthy get elected. Ocasio-Cortez said she told the faction: "Absolutely not."

Rep. Andy Harris, R-Md.: The outlier in the Maryland delegation was one of nine Republicans who signed a letter Sunday saying the times called for a "radical departure from the status quo" and said "McCarthy bears squarely the burden to correct the dysfunction he now explicitly admits across that long tenure."

Anna Paulina Luna, R-Fla.: One of five freshman members to vote against McCarthy, Luna was one of the nine to sign the Sunday letter that said McCarthy's negotiations have been "insufficient."

Mary Miller, R-Ill.: The second-term Illinois representative has been quiet on her vote. But former Rep. Rodney Davis — whom Miller defeated in the GOP primary — told CNN on Tuesday that "I don't think anybody from Illinois would be surprised by that vote." Like the majority of other McCarthy defectors, Miller had Trump's endorsement, denies results of the 2020 presidential election, objected to the 2020 Electoral College results and is a member of the House Freedom Caucus.

Ralph Norman, R-S.C.: While some of the 21 may be waiting to see which way the wind blows, Norman has been an early and hard "no" on McCarthy. The core of his problem with McCarthy is how to budget.

Andy Ogles, R-Tenn.: One of the five incoming freshmen opponents, Ogles so far hasn't publicly indicated why. He was also, though, one of the nine signers of the letter saying McCarthy hadn't done enough to meet conservatives' demands.

Scott Perry, R-Pa.: Perry is chairman of the GOP Freedom Caucus – of which 19 of the 21 non-McCarthy voters are members. He said, as of late November, that he was pushing McCarthy to make rules changes that gave more power to members and weaken the speakership.

Matthew Rosendale R-Mont.: He said as early as November that he wouldn't be supporting McCarthy. He's critical of McCarthy for wanting to "maintain the status quo" for not giving members more power over legislation, like allowing debate on the floor instead of through committees. A spokesperson has said Rosendale would only vote for McCarthy "under extreme circumstances."

Chip Roy, R-Texas: He's been vocal in his opposition to McCarthy for months – unless he would support rules changes that would open up floor debate and give members more say. Roy said he was upset about spending bills passing without debate, particularly an aid package to Ukraine.

Roy has spearheaded the drive against McCarthy for months, nominating Biggs for party leader over McCarthy in November. Thirty members joined him in that preliminary vote, but McCarthy still won handily. Roy said Wednesday night he thinks he can bring along 10 members if demands are met, per CNN. But that still wouldn't be enough to put McCarthy over the top.

Rep. Keith Self, R-Texas: Another of the five incoming freshmen to vote against McCarthy, even though a couple months ago, he strongly backed him. McCarthy even stumped for him in Texas, and McCarthy's PAC donated $5,000 to Self's campaign.

Rep. Victoria Spartz, R-Ind.: Spartz, a Ukrainian-born member who has been criticized by some in her conference for her conduct on a congressional delegation to Ukraine and her criticism of Ukrainian President Zelenskyy, was the only member to vote "present" on one of the votes. She said on CNN Wednesday she thinks McCarthy has worked hard but needs to listen to the opposition's concerns, "come to agreement and not waste everyone's time." [Copyright 2023 NPR]