WASHINGTON — On the eve of the House’s vote to pass a far-reaching $1.5 trillion tax cut, Speaker Paul D. Ryan of Wisconsin placed a hasty phone call to his state’s senior senator, Ron Johnson, in hopes of resolving an unlikely conflict in his own back yard.

Mr. Johnson had become the first Senate Republican to say publicly that he could not vote for the Senate’s version of the tax bill. During the phone call on Wednesday afternoon, Mr. Ryan, who had campaigned heavily for Mr. Johnson in 2016, posed an essential question, according to the senator: “What are you going to need?”

What Mr. Johnson needs, he said in an interview from Wisconsin on Friday, is for the bill to treat more favorably small businesses and other so-called pass-through entities — businesses whose profits are distributed to their owners and taxed at rates for individuals. Such entities, including Mr. Johnson’s family-run plastics manufacturing business, account for more than half of the nation’s business income, and the senator says the tax bill would give an unfair advantage to larger corporations.

“I just have in my heart a real affinity for these owner-operated pass-throughs,” he said. “We need to make American businesses competitive — they’re not right now. But in making businesses competitive, we can’t leave behind the pass-throughs.”