Sen. Steve Daines Steven (Steve) David DainesMcConnell locks down key GOP votes in Supreme Court fight Will Republicans' rank hypocrisy hinder their rush to replace Ginsburg? Toobin: McConnell engaging in 'greatest act of hypocrisy in American political history' with Ginsburg replacement vote MORE (R-Mont.) on Monday became the second GOP senator to oppose the upper chamber's tax bill in its current form, raising concerns it does more to help corporations than other types of businesses.

"Sen. Daines has concerns with how the tax bill looks at main street versus large corporations," an aide to the Montana Republican said. "The Senator wants changes to the tax cut bill that ensure main street businesses are not put at a competitive disadvantage against large corporations."

The aide added that while Daines is currently a no on the measure, he "remains optimistic and is continuing to work with colleagues."

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Daines joins Sen. Ron Johnson Ronald (Ron) Harold JohnsonThis week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report Democrats fear Russia interference could spoil bid to retake Senate MORE (R-Wis.) in rejecting the current version of the bill.

The two senators are pushing for lawmakers to do more to help "pass-through" businesses whose income is taxed through the individual tax code. Pass-throughs can take the form of sole proprietorships and partnerships and include many small businesses.

Under the Senate Republican bill, the corporate tax rate would be cut from 35 percent to 20 percent. While the bill would also provide a 17.4-percentage point deduction for pass-through businesses, those businesses would still see higher effective tax rates than corporations.

Daines and Johnson are working with other GOP lawmakers and the White House to make changes to the bill so that they can ultimately vote for it.

President Trump said on Twitter Monday that changes could simplify the pass-through provision and make it work better.

Daines retweeted Trump's comment and added that "it was good to speak with @realDonaldTrump this weekend working through these concerns."

Senate Republicans are expected to start floor consideration of the tax bill this week. If every Democrat votes against the measure, no more than two Republicans can also oppose it and still allow Vice President Pence to cast a tie-breaking vote.

Daines and Johnson are the only two lawmakers that have said they currently oppose the bill, but others have expressed concerns over the bill's impact on the deficit and its repeal of ObamaCare's individual mandate.