Senate Majority Leader Mitch McConnell (R-Ky.) speaks to reporters about the GOP tax bill following a closed-door strategy session on Capitol Hill on Tuesday. (J. Scott Applewhite/AP)

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

The move, which needs to gain the support of a broad swath of Republicans in the House and Senate, would lower taxes for top earners throughout the country, potentially addressing the concerns of two GOP constituencies about separate tax legislation passed by the House and Senate.

Wealthy individuals in New York, California and other high-tax states had complained that their taxes might go up under the plan, which curtails the ability of taxpayers to deduct state and local taxes. And conservative House Republicans had said it did not go far enough to bring down top rates — long a principle of Republican economic orthodoxy.

But there were signs of immediate resistance to the idea from at least two Senate Republicans, and the GOP can only afford to lose the support of one if they want to pass the bill.

Sen. Susan Collins (R-Maine) said she didn’t want to lower the top income tax rate. “I don’t think lowering the top rate is a good idea,” she said as word circulated about the plan.

“It’s hard to believe the Republicans can make this bad bill even worse, but behind closed doors, that’s exactly what they seem to be doing,” said Senate Minority Leader Charles E. Schumer D-N.Y.). (J. Scott Applewhite/AP)

And Sen. Marco Rubio (R-Fla.) expressed frustration with the idea in a Twitter post, writing 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.”

Talks remained extremely fluid Tuesday night as the move to reduce the top rate emerged as the most prominent, and most controversial, of the changes being seriously considered by lawmakers as they sought to reconcile House and Senate tax bills by the end of the week.

It was not immediately clear whether the negotiations might be affected by Democrat Doug Jones’s projected victory over Republican Roy Moore in a special U.S. Senate race in Alabama.

Republicans insisted Jones’s upset win Tuesday night would make no difference. Jones is not expected to be seated until after Christmas, and until that happens the Senate seat is occupied by appointed Republican incumbent Luther Strange, a reliable GOP vote.

Yet given Republicans’ already ­razor-thin margin on the tax legislation, it was possible that the Jones win could buoy Democrats or empower wavering Republicans. If nothing else, the unexpected outcome seemed likely to increase the GOP’s determination to wrap up by the end of next week as planned.

Amid GOP negotiations earlier Tuesday, the other most significant change under consideration was to the corporate tax rate, which lawmakers now plan to reduce to 21 percent instead of 20 percent. The corporate tax rate is currently 35 percent.

Lawmakers also planned to find a middle ground between how the House and Senate bills treat the mortgage-interest deduction. The new legislation appears likely to allow taxpayers to deduct up to $750,000 in new mortgage interest on homes.

Lawmakers on Tuesday evening stressed that key elements, including the top tax rate, could shift as Republican leadership seeks to deliver a majority of votes in the House and Senate under an aggressive plan to pass a final tax bill by early next week, sending it to President Trump for his signature by Christmas.

Republican leaders were being cautious 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 with just one vote to spare.

Republicans are grappling with sensitive demands from their members. Sen. Ron Johnson (R-Wis.) is pushing for big tax cuts for partnerships and sole proprietorships. And Collins also wants for a vote on health-care legislation that would strengthen the Affordable Care Act marketplaces.

During Senate debate earlier this month, Rubio proposed raising the corporate tax rate to 20.94 percent in exchange for expanding the child tax credit. His effort was rejected by many Republicans at the time, as they alleged raising the corporate tax rate in such a way would hurt economic growth.

Rubio must now decide whether to follow through on his repeated threats and oppose the bill, potentially standing in the way of Trump’s top legislative priority. Or he can go along with the rest of Republicans and risk having his complaints dismissed during future political fights.

Democrats, for their part, lashed into the bill Tuesday evening.

“It’s hard to believe the Republicans can make this bad bill even worse, but behind closed doors, that’s exactly what they seem to be doing,” said Senate Minority Leader Charles E. Schumer (D-N.Y.).

In the current tax code, income above $470,700 is taxed at a 39.6 percent rate for a married couple who file their taxes jointly. Only one in 200 taxpayers pay the top tax rate today, according to the Tax Policy Center.

The tax bill passed by House in November would keep the 39.6 percent rate but only use it for income above $1 million. The Senate bill would apply a 38.5 percent top rate to people earning over $1 million.

It could not be learned at what income level Republicans were considering attaching a new 37 percent rate.

Lawmakers plan to hold their only public, official event to discuss the bill Wednesday, and Trump plans to deliver a closing argument in favor of it at the White House.

Most polls have shown a lack of support among voters for the tax plan, with many Americans saying it is designed in a way that disproportionately benefits the wealthy.

Independent nonpartisan analysis shows the tax plans passed by the House and the Senate would benefit most Americans, at least in the near term, but the wealthiest would see the most gains.

But Tuesday, a senior White House official argued these views would evolve as people personally felt the impacts of the tax cut.

These polls are “not a reflection of what the American people think about what we are doing,” the official said, speaking on the condition of anonymity under the terms of a White House briefing. “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 the tax bill might be seen as tilting too strongly toward 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. 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 also pushed for the lower individual rate. They could have been sympathetic to complaints from the wealthy and conservatives that these changes were necessary to boost economic growth and investment.

Both bills included as their central feature a massive reduction in the corporate tax rate, from 35 percent 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.

“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. 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. They were also discussing the estate tax for inheritances, which the House bill repeals fully and the Senate bill only limits.

House conservatives have been pushing to keep full repeal, but House Ways and Means Committee Chairman Kevin Brady (R-Tex.) 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."

Beyond the estate tax, the Senate bill retains seven income-tax brackets for individuals and families, while the House bill collapsed those brackets to four.

The House and Senate bills also tax partnerships and sole proprietorships differently. And the House bill would eliminate the alternative-minimum tax, which seeks to make sure wealthy individuals are not able to improperly reduce their tax burden, while the Senate bill would not.

Congressional leaders have 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.

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

Heather Long and Jeff Stein contributed to this report.