Jim Jordan keeps pressing on with his bid for House speaker, despite a growing number of Republican votes in each of the first three rounds of balloting.

A list that started at 20 has now grown to 25.

Mr Jordan says he is going to keep trying to convince his party’s holdouts, even if it means working through the weekend. His opponents say they’re not budging.

Something, at some point, has to give.

When faced with what appeared to be a hopeless cause, Steve Scalise – the first Republican pick to replace the ousted Kevin McCarthy – threw in the towel before any ballots had been cast.

Mr Scalise, however, was a more traditional Republican legislator, who had come up through the ranks of his party’s leadership and had made deals and built relationships to become the second-ranking Republican in the House.

Mr Jordan, on the other hand, is a different character. He came up as a political bomb-thrower. He co-founded the House Freedom Caucus, which has used political brinksmanship – under threat of government shutdowns and even a national default on the debt – to bend centrist and establishment Republicans farther to the right.

He also has the backing of Donald Trump and his right-wing populist movement and is embraced by a conservative media ecosystem anchored by Fox News evening talk-show hosts like Sean Hannity.

Where Mr Scalise’s motivations were to cut his losses and maintain his position within the Republican hierarchy, Mr Jordan’s incentives are to ignore the political torpedoes and forge ahead.

If he wins, he becomes the speaker, with all the power and privileges that conveys. If he loses – if his opponents eventually co-operate with Democrats to install some kind of coalition speaker or the Republicans come together on a less controversial alternative – he becomes a martyr for the right-wing cause.

It’s a formula for an extended standoff. And while some of Mr Jordan’s fellow Republicans are grumbling that this deadlock needs to be resolved quickly, there is still almost a month before House inaction would trigger a government shutdown.

It may only be at that point, when the lives of average Americans are disrupted, that this transforms from a Washington drama to a full-blown national crisis.