Sen. John Thune (R-S.D.) talks with reporters on Capitol Hill this month. (Katherine Frey/The Washington Post)

Senior Republican negotiators were close to reaching a deal Tuesday to reduce the tax rate for high-income households from 39.6 percent to 37 percent, blowing past political concerns about aiding the rich in order to ease passage of a $1.5 trillion tax package.

The move, which would still need to gain the support of enough Republican lawmakers in both the House and Senate, follows complaints from wealthy taxpayers in New York and elsewhere that their taxes could go up under the legislation because of other changes it makes to the code  It also follows pressure from conservative House Republicans who complained the tax plan did not do enough to bring down top rates.

Importantly, the changes would go far beyond addressing the complaints of wealthy New Yorkers and Californians and would lower taxes for top-earners across the country.

Republicans were planning to change their proposal to drop the corporate tax rate from 35 to 20 percent. Under the new plan, they would tax companies at a rate of 21 percent, a move that would raise roughly $100 billion.

They also planned to find a middle ground between House and Senate legislation on how much in mortgage interest taxpayers could deduct — eying $750,000 as a likely threshold.

The moves were calculated to deliver Republicans a majority of votes in the House and Senate as lawmakers proceed on an ambitious plan to produce a final tax bill this week and pass it by early next, sending it to President Trump for his signature by Christmas.

But Republican leaders were being cautious on Tuesday to ensure that the changes would not drive away the support of any members, particularly in the Senate, where they hold a slim majority and narrowly passed an earlier version of the tax bill 51-49. It could take several days until they have assurances that all their members are on board.

Late Tuesday, the emerging plan faced immediate blowback when Sen. Marco Rubio (R-Fla.) tweeted that it was wrong for negotiators to reject his plan to expand tax benefits for working families as “anti-growth” when they were fine “to cut tax for couples making $1 million.”

Republicans are dealing with numerous sensitive demands from their members. In addition to Rubio’s demands for an expanded benefit for working families, Sen. Susan Collins (R-Maine) has expressed concern about extending more tax cuts to the wealthy and asked for a vote on a health care bill. Sen. Ron Johnson (R-Wis.) has demanded big tax cuts for partnerships and sole proprietorships.

Each of these members supported the tax measure when it passed the Senate and have expressed they’d like to support the tax bill. GOP leaders need to discern whether any of these members are willing to block the bill if they feel their concerns aren’t met.

Currently, income above $470,700 is taxed at a 39.6 percent rate for a married couple who files their taxes jointly.

The tax bill passed by the House of Representatives in November would keep the 39.6 percent rate but only use it for income above $1 million. The Senate bill would eliminate the 39.6 percent rate and create a new top rate of 38.5 percent, which would go into effect for income above $1 million.

It could not be learned at what income level Republicans were hoping to attach a new 37 percent rate.

GOP aides stressed that no changes would be final until the legislation has formally been filed, which lawmakers are aiming to do on Friday. Lawmakers plan to hold their only public event to discuss the bill Wednesday, and Trump plans to give his “closing argument” for the tax bill Wednesday at the White House. He will be joined by five families from around the country.

A senior White House official disputed there would be any political price for the tax plan, criticizing polls show it is deeply unpopular.

These polls are “not a reflection of what the American people think about what we are doing,” the official said. “Does anyone on the planet actually believe that hard-working Americans don’t want lower taxes and a simple, easy-to-understand tax code?”

The White House and GOP leaders had originally envisioned lowering the top rate to 35 percent, but they relented after concerns that the tax bill might be seen as tilting too strongly toward the wealthy. In late September, the White House and GOP leaders opened the door to retaining the 39.6 percent tax bracket, and House lawmakers inserted it into their bill.

Some close to Trump have warned about the public perception of designing the tax package in a way that appears to cater to the wealthy. Former White House chief strategist Stephen K. Bannon had recommended internally that they consider a 44 percent tax bracket for income over $5 million, but his idea was shot down by others in the White House who said all tax rates needed to come down, even for the wealthy, to spur more economic growth.

After the House and Senate passed their versions of the tax bill, complaints from wealthy Americans — particularly in New York — grew louder, as they believed their taxes could actually go up under the new legislation. That’s because the tax bills would limit the ability to deduct state and local income taxes, among other changes, making it harder for the wealthy to lower their taxable income. Trump has received an earful from friends and supporters in New York, and last week signaled that he could support changes that he said would help a “sliver” of people.

People familiar with the negotiations said House Republicans pushed for the lower individual rate. They could have been more sympathetic to complaints from the wealthy and conservatives that these changes were necessary to boost economic growth and investment. House Republicans has also been the most sympathetic to calls from the wealthy to eliminate the estate tax, though not all Senate Republicans shared this view.

Both bills included as their central feature a massive reduction in the current 35 percent tax rate down to 20 percent. Trump had insisted for weeks that he would not allow anything above a 20 percent rate, but in recent days the White House has showed more flexibility as they tried to help lawmakers get a deal across the finish line.

Ever since the deliberations regarding slightly raising the corporate rate became public, conservative groups have been agitating against raising it over 20 percent. So negotiators face significant crosswinds on the issue, illustrating the pressure they are under as they rush to wrap up a final product.

“We are entering another huge week for tax reform,” House Speaker Paul D. Ryan (R-Wis.) said Tuesday. “Tax reform is what people need right now and I am so thrilled that we are so close to the finish line. We are going to keep at it so we can deliver real tax relief before Christmas.”

Once House and Senate GOP leaders reach an agreement on the design of the tax compromise, they must submit the package to each chamber for votes. That’s why they are treading cautiously on every detail, worried that a single Senate Republican could balk at a change, withdraw support, and put the entire package in peril.

There were a number of other decisions that remained in flux.

They were discussing the possibility of allowing the corporate tax cuts to take effect in 2018 instead of the 2019 date set in the Senate bill. Another was the estate tax, which the House bill repeals fully while the Senate bill only limits. House conservatives have been pushing to keep full repeal, but Brady indicated openness to the Senate approach.

“In the House we feel very strongly about fully repealing the estate tax,” Brady said. “We’re having those discussions with the Senate that took a different approach. They did double the exemption so that helps a lot of family-owned farms and businesses. So that’ll be part of the final agreement.”

Overall, Brady said, “nothing’s final until everything’s final and tax reform is truly a Rubik’s cube.”

Beyond the estate tax, the House and Senate bills have a number of differences that must be resolved.

For example, the Senate bill retained seven income tax brackets for individuals and families, while the House bill collapsed those brackets down to four.

The House and Senate bills also tax partnerships and sole proprietorships much differently. The House bill would also put new limits on how much mortgage interest a household can deduct from their income, while the Senate bill would not make changes.

And the House bill would eliminate the alternative-minimum tax, while the Senate bill would not.

“We’re narrowing those differences, we’re trying to take things off the table so we can narrow those differences,” Sen. John Cornyn (R-Texas).

Congressional leaders have already signaled how they plan to resolve some differences between the two bills. For example, the Senate bill would repeal the individual mandate of the Affordable Care Act, while the House bill would not. But House leaders have suggested they like that change to the health care law and support including it in the final bill.

Heather Long contributed.