Ahead of the opening day of the new Congress, Representative Chip Roy, who was refusing to commit to voting for Speaker Mike Johnson’s re-election, took an intense phone call from President-elect Donald J. Trump.

Mr. Trump was blunt with Mr. Roy, the ultraconservative Texas Republican who had recently defied him and voted against his desired spending and debt deal: He would pull back on the abuse he had unspooled online, including a threat to recruit a primary opponent to unseat him, if Mr. Roy would fall in line behind Mr. Johnson — and generally get on board with the Trump agenda.

“I will if you’re good to me,” Mr. Trump told Mr. Roy, according to two people familiar with their conversation. “But you’re not being very good to me.”

Mr. Roy ultimately voted for Mr. Johnson, sparing the party a bloody leadership fight just before Mr. Trump took office. And these days, Mr. Roy has been supporting Mr. Trump’s agenda. In return, the president has, as promised, stopped savaging him in public.

It was Mr. Roy who helped convene a group of fiscal conservatives to meet with Mr. Trump last week at the White House to discuss the temporary spending bill that the president needs them to support to avoid a government shutdown after midnight on Friday. And it was Mr. Roy who made the most aggressive case in the meeting that members of the group, many of whom are uniformly opposed to such stopgap funding measures, should back the plan.