He said he's concerned that there isn't enough information available to make an informed vote. He also said the plan may benefit corporations more than other smaller businesses.
"I don't have the information on how much it would cost, how many pass-through businesses are being left behind that do compete globally. I can't get the information. I've been asking. They don't give it to me," Johnson said.
"I got a call from President Trump last night. He's telling me 'I'll get the information. I'll meet with Treasury officials today. I will work my tail off over the weekend to fix this problem so we can move forward with pro-growth tax reform,'" Johnson added.
Johnson appeared on CNBC before the Joint Committee on Taxation released on Thursday its latest look at the GOP Senate bill.
Trump has been pushing lawmakers to pass a tax bill, which he says would ease the burden on middle-class Americans and give U.S. businesses incentives to invest at home.
Johnson said the process for working on the bill has not been transparent. "It's not a real good process," he said. "The House is voting on theirs today. We're going to be voting on ours right after Thanksgiving."
Sens. Susan Collins of Maine, Bob Corker of Tennessee and John McCain of Arizona have also voiced concerns over the Senate's tax plan. They refused to say whether they would ultimately vote for the bill.