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.