Just minutes after Speaker Mike Johnson could exhale, having put down a short-lived conservative revolt and won re-election to his post on Friday, hard-right lawmakers sent him a letter.

It was not congratulatory.

They had only voted for him, they wrote, “because of our steadfast support of President Trump and to ensure the timely certification of his electors.”

“We did this despite our sincere reservations regarding the speaker’s track record over the past 15 months,” lawmakers in the ultraconservative House Freedom Caucus continued, appending a list of three major complaints about Mr. Johnson and seven policy dictates they demanded he adopt.

Welcome to the 119th Congress.

“I just expect intramural wrestling matches to be kind of the norm,” Representative Mark Amodei, Republican of Nevada, said as he walked off the House floor after Mr. Johnson’s whipsaw election to the speakership.

Ever since he ascended to the top job in the House after many of those same conservatives ousted his predecessor, Mr. Johnson has had one of the hardest jobs in Washington. Now, with total Republican control of government and President-elect Donald J. Trump’s enormous domestic agenda at stake, he is facing his toughest test yet.

Mr. Johnson will be responsible for pushing through Mr. Trump’s economic plans, including one or more huge bills that lawmakers say they want to simultaneously increase the nation’s borrowing limit, extend the tax cuts Mr. Trump signed into law in 2017, cut federal spending, and put in place a wide-ranging immigration crackdown.

Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.

Thank you for your patience while we verify access.

Already a subscriber? Log in.

Want all of The Times? Subscribe.