The newly elected US House of Representatives convenes; the outgoing speaker dismisses the previous chamber; the majority party elects its leader as speaker, and the new speaker in turn swears in members-elect. Then, Congress gets down to business – legislating, budgeting and oversight.

Not so this time around. Three days and six ballots later, the House has yet to choose a speaker, with top Republican Kevin McCarthy failing to secure a majority as far-right opposition against him has persisted.

As the chamber heads to a seventh vote on Thursday, uncertainty still hangs over McCarthy’s bid for the speaker’s gavel. The Republican’s thin majority in the chamber has meant that a few GOP dissenters can upset the party’s agenda.

Since the House adjourned on Wednesday evening, there were reports of movement towards a resolution, but also continuing opposition to McCarthy from some members.

“No deal yet, but a lot of progress,” McCarthy told reporters on Wednesday as Republicans continued to negotiate to find a solution to the deadlock.

In three votes on Wednesday, the Republican leader – a California Republican – received 201 votes, well short of the 218-vote majority he needed.

His Republican detractors nominated Florida Representative Byron Donalds, who received 20 votes, while Democrat Hakeem Jeffries got 212.

The Republican dissenters have numerous demands to agree to switch their votes and back McCarthy, including changing House rules to allow any member to bring a no-confidence vote in the speaker.

They also want a bigger say on the House Rules and Appropriations committees, which would allow them to influence the US government budget and help decide which bills can move forward in the chamber.

Republican Congressman Dan Bishop, who has been voting against McCarthy, told MSNBC on Thursday that the party was working for “continued improvements” to the legislative progress, which he said has “seen progress”.

Yet, some anti-McCarthy holdouts appear to be confident that they will be able to continue to derail his bid.

“We’ve only increased with votes in our vote share in opposition to Kevin McCarthy. We suspect that that trend is likely to continue,” Congressman Matt Gaetz, a ringleader in the Republican dissenters’ camp, told Fox News on Wednesday.

Although the House has not failed to elect a speaker in the first round since 1923, anti-McCarthy Republicans are portraying the deadlock as a healthy debate that is beneficial to US democracy.

But the House cannot function without a speaker. So how does this crisis end?

As things stand, the only way to resolve the issue is for a candidate to win a majority. At 20 votes, Donalds – the GOP rebels’ nominee – is far from that threshold, and with only two years of US House experience under his belt, he is considered a longshot candidate at best.

McCarthy remains a more realistic option, but he needs to convince enough dissenters to back him. If he fails to do so and withdraws, Republicans may be able to find a consensus candidate.

So far no realistic alternative to McCarthy has been put forward, but US commentators have suggested that key Republican Steve Scalise, who is currently in the McCarthy camp, could be an option.

The House can elect someone from outside Congress altogether as speaker. Former Michigan Representative Justin Amash, who left the Republican Party in 2019 before retiring from Congress, has offered to take the job as a “nonpartisan” speaker.

Amash has been a longtime critic of the centralisation of power in the hands of the speaker, calling for more debates and expanding the influence of individual members in the chamber.

If neither party has the votes to elect a speaker of the House, I’d be happy to serve as a nonpartisan speaker who ensures the institution works as it’s supposed to—a place where all ideas are welcome and where outcomes are discovered through the process, not dictated from above.

— Justin Amash (@justinamash) November 15, 2022

Amash’s bid is also most likely to fail. The former congressman lost his status as a rising star in the Republican Party after regularly criticising then-President Donald Trump before leaving Congress.

There have also been suggestions that Democrats and Republicans can join together to choose a moderate speaker. However, in six ballots Democratic lawmakers have stayed unanimous in backing Jeffries and ruled out helping Republicans elect a speaker.