Republicans have long promised tax cuts and see enacting them as critical to their prospects of retaining power in Washington in the November 2018 congressional elections, particularly after failing to meet their promise to repeal the Affordable Care Act, better known as Obamacare.
But it will be a challenge in the 100-seat Senate, where Republicans have only a 52-48 majority.
Senators Jeff Flake and James Lankford are among the four Republicans considering opposing the plan, Time reported.
A Lankford spokesman said he was "eager to work with colleagues to pass tax reform."
Flake, who often clashes with Trump and has announced he will not seek re-election next year, told Reuters on Thursday he was "more worried about the fiscal problem" than other issues.
Several other senators, including Ron Johnson and Susan Collins, who helped sink the Republican effort to repeal Obamacare, have expressed concerns.
Johnson announced his opposition because of what he said were unequal rates for small businesses and non-corporate enterprises known as "pass-throughs," versus corporations. He is working with the White House to fix the issue, he told Reuters.
Senator John McCain, a Republican who also voted against the healthcare overhaul effort this summer, and his colleagues Bob Corker and Lisa Murkowski, are also considered critical votes.
Nonpartisan congressional analysts say the provision to repeal the health insurance mandate in the Senate version would drive up premium costs and cause some 13 million Americans to lose coverage.
The Senate plan also sets individual tax rate cuts to expire while reductions for corporations are permanent.