The lawmakers attracting the most concern from leadership and the White House are Sen. Ron Johnson, R-Wis., and Steve Daines, R-Mont., who say the current version of the bill favors corporations over other businesses.
There are numerous members demanding changes, and their needs don't all overlap. Together, the requests put Republican leaders in a difficult position, as they attempt to accommodate individual holdouts on a one-off basis without losing other members or creating a situation in which the bill collapses under the weight of disparate demands.
Adding to the leaders' difficulty, the total size of the tax plan cannot be more than $1.5 trillion over a decade, so adding new benefits could force Republicans to find ways to raise additional revenue. Presently, they have only roughly $80 billion in wiggle room to use, a small sum because many of the changes would be spread out over 10 years.
The four people spoke on the condition of anonymity because they were not authorized to discuss the internal discussions.
Johnson and Daines want changes to the bill they believe would help certain companies that file through the individual income tax code. These companies, often known as "pass-throughs," can be small businesses but also include larger firms with many employees. There are millions of such companies in the United States, and they account for the bulk of U.S. firms.
Currently, in the Senate bill, these companies are allowed to deduct 17.4 percent of their income from their tax liability. Negotiators are looking at expanding that credit up to about 20 percent, two of the people said.
It's unclear if Johnson would accept these changes as sufficient, and a final decision hasn't been made. If Republican leaders believe Johnson's demands have become too unreasonable, they could try and forge ahead without his vote.
Spokesmen for Johnson and Daines didn't have an immediate comment on the discussions.
There are 52 Republicans in the 100-seat Senate, and GOP leaders can afford to only lose two votes if they want to pass their bill because Democrats are expected to unite in opposition against it. Typically, tax bills require 60 votes in order to clear procedural hurdles, but Republicans are trying to pass the package through a process known as "reconciliation" that requires only a majority of votes.
At least six GOP members have raised concerns about specific provisions in the GOP tax bill, though none has flatly said they plan to vote against it this week. Johnson came closest, saying he opposed the measure but later suggesting he could support it with changes.
Senate Republicans have received criticism because their tax plan does not allow individuals, families, and pass-through companies to deduct their state and local taxes from their taxable income. The tax plan does allow firms that pay corporate income taxes to deduct their state and local taxes.
To create more parity, negotiators are considering putting new curbs on the ability of corporations to deduct state and local taxes from their income. The money this change frees up could be used for other tax benefits for companies.
Senate Republicans are also seriously considering a change requested by Sen. Susan Collins, R-Maine, which would allow Americans to deduct $10,000 in local property taxes from their taxable income. This provision was in a bill that passed the House of Representatives, but it is not in the Senate bill. Though Collins has voiced the most concerns about its absence, other members have quietly said they also want the change to be made.
Making this change could cost more than $100 billion over 10 years and probably would require Republicans to find new money to offset it.
The changes could be made — or attempted to be made — over the course of the week.
Voting on the tax measure is scheduled to begin Tuesday, as the Senate Budget Committee plans to take a procedural step that afternoon that would effectively send the tax bill to the Senate floor. But Johnson is on the budget panel, and he could demand changes by Tuesday in order to win his vote. If he blocks the tax bill in the Budget Committee and is joined by Sen. Bob Corker, R-Tenn., who has raised separate concerns, the package could quickly die.
The tax package is a combination of changes for companies and individuals that would lower rates in a way Republicans say would lead to more growth and hiring. But Democrats have said the tax changes are uneven, offering long-term benefits for companies and the wealthy and temporary tax cuts for individuals and families. It would add between $1.4 trillion and $1.5 trillion to the debt over 10 years, budget forecasters have said, though Democrats and Republicans differ over how much economic growth the plan would trigger.
The Washington Post's Erica Werner contributed to this report.