WASHINGTON — House Republicans on Friday quietly made changes to their far-reaching tax overhaul: Now its tax cuts would be less generous for many Americans.

A day after the GOP unveiled its plan promising middle-class relief, the House’s top tax-writer, Rep. Kevin Brady, released a revised version of the bill that would impose a new, lower inflation “chained CPI” adjustment for tax brackets immediately instead of in 2023. That means more income would be taxed at higher rates over time — and less generous tax cuts for individuals and families.

The change, posted on the website of the Ways and Means Committee, reduces the value of the tax cuts for ordinary Americans by $89 billion over 10 years compared with the legislation released with fanfare Thursday.

As wages rise, middle-class taxpayers would have more of their income taxed at the 25 percent rate instead of at 12 percent, for instance.

“The bill’s like a dead fish: The more it hangs out in the sunlight, the stinkier it gets,” Senate Democratic Leader Chuck Schumer pronounced after word of Brady’s change. “The more people learn about this bill, the less they’re going to like it.”

The change to the plan frees up money for Brady, R-Texas, the committee’s chairman, to use to address concerns by lawmakers when changing the bill further next week. The Ways and Means panel begins work on Monday, a final bill-writing process expected to take four days.

Brady on Friday called it “a challenge of a lifetime legislatively.”

President Donald Trump and the Republicans are driving to push through a major tax-cutting bill this year to secure a legislative accomplishment, following their stinging failure to overturn and replace the Obama health care law. The Republicans, facing increasing pressure to produce a marquee legislative victory before next year’s elections, are promoting their tax plan as a spark for economic growth and a boon to the stressed middle class.

While Trump and House Republican leaders stand united behind the plan, rank-and-file GOP lawmakers are divided and complaining about its potential blow to homeowners and the loss of a prized deduction that especially hits high-tax states.

And Trump is pressuring Republicans to repeal a health-care law penalty in the tax rewrite, a step that Brady indicated is politically problematic. Some of the GOP lawmakers agree.

Brady said Friday the president had spoken to him twice by phone and once in person, imploring him to scrap the so-called individual mandate that requires Americans to obtain health insurance or face a penalty.

“The president feels quite strongly about including this at some step,” Brady said in an interview with Politico.