Jim Jordan’s rapid rise has been cheered by Trump and the far right. Could it soon make him speaker?

Rep. Jim Jordan has such a reputation as a political brawler that former House Speaker John Boehner once said he’d never met someone “who spent more time tearing things apart.”

Now, nearly a decade after Boehner stepped down in the face of a conservative revolt, it is Jordan who is trying to bring the Republican Party together to win the speaker’s gavel.

A favorite of former President Donald Trump and darling of the party’s rabble-rousing base, Jordan’s path to the U.S. government’s third-highest office is by no means certain in a House Republican conference...