Sen. Mike Crapo, R-Idaho, is an important player as the Senate works to advance President Donald Trump's signature piece of legislation.

As Senate Finance Committee chair, Crapo and his panel are focused on the costs and savings of the "one, big, beautiful bill" that passed the House.

That includes the extension of 2017 tax cuts, currently scheduled to expire at year's end.

Other pivotal items include the cap on state-and-local tax (SALT) deductions, Trump's campaign promise of no tax on tips, and proposed changes to improve Medicaid.

"Mike Crapo is probably one of the three most well-respected members of the Republican caucus," Sen. John Kennedy, R-La., told Politico. "People trust him. He listens. He tells you the truth. He tries to be inclusive, sometimes to a fault.

"He's quiet. He's really, really smart."

Sen. Mike Rounds, R-S.D., also spoke highly of Crapo.

"[He] puts the time in on it. He's low-key, but he is a connector, a facilitator," Rounds said. "He doesn't need the spotlight, but he is very, very effective."

Crapo could begin briefing colleagues on bill text as soon as Monday, Politico reported, though a full tax package may not be ready for release until early next week.

He has remained tight-lipped about how he plans to find an approach that will pass the Senate but not upset members of the House, where the chamber's version of the bill passed by one vote.

"I'm just not going to comment," Crapo said after being asked how he planned to make sure the Trump tax cuts are made permanent, Politico reported.

Asked about potential tweaks to House Medicaid language, Crapo said: "We're working that right now. I'm not going to get into the details."

Asked about negotiations concerning the SALT deduction being increased to $40,000 from $10,000, Crapo said: "We're looking at the entire bill."

Following a meeting last week with Trump, Crapo said, "All the talk about how this bill is going to generate an increase in our deficit is absolutely wrong."

Crapo's reputation is that of a patient person who likes to slowly build agreement among his committee members.

"Crapo is a very thoughtful and deliberate lawmaker who has strong views on tax policy himself, but also who cares about what his committee members want," said Joe Boddicker, a former tax counsel for Senate Finance Republicans under Crapo, Politico reported.

"He will try to incorporate the feedback from them, and he puts a high premium on that feedback … so it'll be a group product, one that reflects the viewpoints of the committee membership."

Reuters contributed to this story.