Will Jim Jordan or Steve Scalise — or even Kevin McCarthy — be the next speaker of the House?

Once more unto the breach for the U.S. House of Representatives.

After taking 15 ballots to elect a speaker in January — the first multi-ballot contest in a century — Congress’s lower chamber will once again gather this week to pick a new leader. This marks only the sixth time since 1913 that the House has had to elect a new speaker during a sitting Congress, but all previous cases came about due to the speaker’s death or impending resignation. This time, though, the vacancy is the result of last week’s successful motion to vacate the speakership. Precipitated by a small faction of GOP members, the measure narrowly ousted Republican Speaker Kevin McCarthy with support from House Democrats.

The majority Republican caucus will now turn to picking a new speaker, starting with an internal party meeting in which the GOP will attempt to coalesce around a single nominee. Two contenders have emerged: House Majority Leader Steve Scalise of Louisiana, a more amiable veteran of party leadership, and Rep. Jim Jordan of Ohio, who has a more fiery, insurgent reputation. While both are solidly conservative, their differing appeals could split the GOP along multiple lines, including ideology and proximity to the party’s establishment. However, other options could be in the mix — including a potential comeback by McCarthy — and with many House Republicans still publicly uncommitted, much uncertainty remains about how the speaker vote might play out.

At this point, Jordan has the upper hand among Republicans who’ve publicly endorsed a speaker candidate, based on members’ statements and other reporting compiled by 538’s Nathaniel Rakich. In this, Jordan has undoubtedly benefited to some extent from an endorsement by former President Donald Trump. Following Trump’s announcement on Friday, a handful of very conservative members shifted from publicly supporting Trump for speaker to supporting Jordan. As of 4 p.m. Eastern on Tuesday, Jordan had 47 public supporters while Scalise had 31, while 136 Republicans remained uncommitted. A small number of other members have expressed support for returning McCarthy to office or, in the case of Georgia Rep. Marjorie Taylor Greene, have said they’ll back Trump, although neither is a declared candidate.

These marks leave Jordan and Scalise well short of the votes they’ll eventually need for victory. Under House rules, the winning speaker candidate must attain a majority among all representatives. Assuming full attendance, the majority threshold is 217 in the 433-member House (Republicans have a 221-to-212 seat majority, with two vacancies). However, the majority line is determined by the votes cast “for a person by name,” so if a member were to vote “present,” that would lower the majority threshold. As a result, in practice, a winning GOP candidate will need a minimum of 213 votes to surpass the 212 votes Minority Leader Hakeem Jeffries will likely receive from Democrats, which means no more than eight Republicans can vote present.

That said, many Republicans are hoping that the caucus will head into a floor vote united behind whomever wins the vote at the upcoming internal party meeting. It may be no simple feat for Jordan or Scalise (or anyone else) to stitch together a majority, however, based on how their support has generally broken down along ideological and insider-outsider lines. Overall, Jordan’s support has mostly come from the more conservative and anti-establishment wing of the GOP caucus, while Scalise’s backers are more concentrated among members who are less ideologically conservative and closer to the party establishment.

We can see this using DW-NOMINATE, a metric political scientists often employ that measures the views of members of Congress based on their voting records. (DW-NOMINATE’s first dimension describes how liberal or conservative members are and, in our current era, the second dimension reveals to some extent how closely aligned members are with their party’s establishment.) By this metric, the average Jordan backer is more conservative than 69 percent of House Republicans, and more anti-establishment than 73 percent of them. By comparison, Scalise’s average supporter is more conservative than only 37 percent of the GOP membership, and more anti-establishment than just 30 percent of it.

The split also shows up in the choices made — or not made — by some of the prominent caucus groups within the House GOP. Twenty-eight of the 45 or so members (the group doesn’t publicize its membership) of the insurgent-minded and very conservative House Freedom Caucus have endorsed Jordan, who co-founded the group, while just one has backed Scalise. Conversely, nine of the 60-plus members of the less combative and more center-right Main Street Caucus have backed Scalise, versus five who’ve endorsed Jordan and five who’ve backed a return by McCarthy.

Looking ahead, Scalise likely hopes that his less conflictual style and pitch that he can unify the party will make him attractive to the disproportionate number of Republican members who aren’t notably anti-establishment (the many gray dots in the upper half of the chart). He’s also played up his fundraising record, which is stronger than Jordan’s. Considering money is vital to winning campaigns and McCarthy was known for his prodigious fundraising hauls, this is not a small concern. Scalise could also have a geographical edge if he can coalesce support among many Republicans from the South, who make up half of the House GOP. That looks like a big if right now, however, as Jordan has a 26-16 edge among Southern Republicans who’ve endorsed, in part because Republicans from the South tend to be more conservative. Scalise has other challenges, too, such as the fact some McCarthy allies have worked against him behind the scenes, partly because of a long-standing McCarthy-Scalise leadership rivalry. Some Republicans may also have concerns about how Scalise’s health — he’s battling multiple myeloma, a blood cancer — could affect his ability to carry out the speaker’s very active day-to-day role.

Meanwhile, Jordan’s challenge is to expand beyond the low-hanging fruit of more conservative and anti-establishment members from whom he’s primarily garnered support. Thus far, about two-thirds of his supporters come from the most conservative third of the party, based on DW-NOMINATE, while only 11 of the 100 least conservative members have endorsed Jordan. And outside of a handful of fellow Ohioans, very few establishment-inclined Republicans have endorsed Jordan. Additionally, it remains unclear if Jordan can branch out and win over some of the more electorally vulnerable members, who tend to have less conservative voting records. Take the 34 Republicans in districts that President Biden would have either carried or lost by less than 5 percentage points to Trump in 2020. Thus far, only three have endorsed Jordan, and only one hails from a seat Biden won — scandal-ridden New York Rep. George Santos, whose time in office probably won’t last beyond this Congress.

Now, these members have mostly remained mum about their plans. After all, Scalise has just five votes from this group, while McCarthy has three. But many of these members may hesitate to vote for Jordan, whose pugilistic style prompted former Republican Speaker of the House John Boehner to call him a “legislative terrorist.” By comparison, Scalise’s fundraising acumen could be of particular importance for swing-seat members facing expensive races. Still, Jordan could win over some of them because of his perceived loyalty to McCarthy, as the ousted speaker was popular among many swing-seat members.

Yet concerns about House chaos amid a war between Israel and Hamas have cracked open the door to a surprising McCarthy comeback. Following his ouster, McCarthy said he would not be a candidate for the speakership, but he’s also said that he would do whatever the GOP caucus wants — and he’s certainly been acting like a party leader in the wake of the Middle East conflict. And some Republicans are angling to put him forward as a speaker candidate, especially because they worry the House will need to act soon to send more aid to Israel. To be clear, a McCarthy renaissance remains unlikely because it would require the Republicans who ousted McCarthy in the first place to acquiesce to his return in some capacity. But the possibility of a deadlock could create an opening for an alternative candidate, such as McCarthy, acting Speaker Pro Tempore Patrick McHenry or perhaps someone like Oklahoma Rep. Kevin Hern, who won votes during the January speaker balloting and looked set to run for the speakership this time around before backing out.

Two final scenarios are extremely unlikely but deserve a short word. Trump does have one public endorser right now in Greene, but the House has never chosen someone who wasn’t a sitting member as speaker. So while Trump has bucked history before, Speaker Trump isn’t happening. Additionally, while wannabe Hollywood writers may want to think that a handful of moderate Republicans could join Democrats to form a coalitional House majority, that’s difficult to imagine in our heavily polarized and partisan political environment. Any Republican who broke to vote with Democrats would, in effect, be making a retirement announcement or would risk a near-certain primary challenge in 2024. Moreover, a 538 review of roll call data found no Democrat or Republican has crossed party lines to vote for a speaker candidate from the other party in the post-World War II era except for maverick Democratic Rep. James Traficant, who voted for Republican Speaker Denny Hastert in 2001.

The uncertainty about the GOP’s ability to come to agreement on a speaker has some Republicans looking to change the party rules for nominating candidates, with an eye on avoiding the multi-ballot fight the GOP experienced in January. On Friday, 94 House Republicans backed raising the level of support a candidate needs in the party caucus to become its speaker nominee before the House goes into session to elect a speaker. Currently, a candidate only needs a majority, but if a candidate needs a higher threshold, that could allow the party to move closer to unanimity — or something close to it — behind closed doors before publicly voting for speaker. Yet some Scalise supporters are suspicious that this proposal could aid Jordan, as Jordan endorser Texas Rep. Chip Roy is among one of the primary backers of this change. Tellingly, a much larger share of Jordan’s endorsers (nearly two-thirds) have signed onto this effort than Scalise’s backers (less than one-third).

There seem to be more unknowns than knowns at this point in the House GOP’s speaker contest, but we do know that some history could be made. Should Jordan or Scalise win, either will arguably be the most conservative speaker the House has seen — especially Jordan. And while Republicans are debating making it harder to vacate the chair again, the eventual winner could end up standing on the same trap door that dropped McCarthy out of the speakership. That could very well mean an even more conservative GOP-run House, which could raise the chances of a government shutdown in November and further threaten future aid to Ukraine in its war against Russia.

Nathaniel Rakich contributed research.