House Ways and Means Committee Chairman Kevin Brady (R-Tex.) sets down a copy of the current tax code as he and the committee’s ranking Democrat, Rep. Richard E. Neal (Mass.), prepare for the first markup hearing of the proposed GOP tax reform legislation Monday. (Chip Somodevilla/Getty Images)

House Republicans on Monday again rejected President Trump's push to use their tax bill to repeal a critical piece of the Affordable Care Act, instead making only modest changes to their legislation as they attempt to move it closer to a vote on the House floor.

House Ways and Means Committee Chairman Kevin Brady (R-Tex.) offered an amendment that would tweak the way the bill would tax the earnings of investment managers, cross-border transactions by multi­national corporations and the endowments of private universities.

The amendment did not make other, more costly changes to business taxation or repeal the Affordable Care Act's insurance mandate, which requires most Americans to obtain some form of health insurance.

Brady said at a day-long Ways and Means markup session Monday that "we are not including various health-tax related measures as part of our tax reform efforts," though he did not specifically rule out repealing the ACA's individual mandate.

"We will move to these important policies separately and immediately after conclusion of our tax reform efforts," Brady said, referring to bipartisan efforts to repeal ACA taxes on medical devices, over-the-counter drugs and health insurance premiums.

Trump had personally pushed Brady to include the mandate repeal, a change nonpartisan analysts say would save the government more than $400 billion over a decade but would also leave 15 million more Americans without health insurance. The plan would give Republicans more flexibility in crafting their bill, but it would complicate the bill's already difficult path through the Senate, where internal Republican divisions and unanimous Democratic opposition have thwarted multiple efforts at repealing the heath-care law.

Brady's changes, which were adopted on a party-line committee vote late Monday, came as Republicans battled new evidence that their tax plan, which they are promoting as a middle-class tax cut, will instead deliver uneven benefits to American workers while delivering outsize benefits to corporations and the wealthiest tier of individuals.

Thomas A. Barthold, chief of staff of the nonpartisan congressional Joint Committee on Taxation, testified Monday that up to 38 million Americans with annual incomes between $20,000 and $40,000 would, on average, see a tax increase starting in 2023 under the House GOP plan.

The Tax Cuts and Jobs Act, the legislative centerpiece of President Trump's economic agenda, aims to deliver a $1.5 trillion tax cut to stimulate economic growth, and Republicans have promised an immediate $1,100 tax cut for a family of four making $59,000. The cliff in 2023, they argue, is due to the planned expiration of a tax credit that Congress will most likely act to extend. But several Democrats on the panel quizzed Barthold, who testified on his office's fiscal analysis of the plan, on the apparent temporary nature of the bill's benefits for some middle-class families.

Barthold also testified that the bill, if passed, would have the immediate impact of greatly reducing the number of taxpayers who itemize their deductions — from the current rate of 29 percent to a projected 6 percent in 2018.

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That reflects the GOP plan's substantial increase in the standard deduction, which could mean simpler filing for tens of millions of taxpayers — a Republican priority. But the drastic reduction in itemization could carry major implications for the housing and nonprofit sectors, which have respectively come to rely on tax deductions to encourage taxpayers to buy homes and donate to charity.

The debate over the middle-class benefits of the bill came as House Republican tax writers negotiated behind the scenes to keep the legislation on track.

The suite of changes Brady unveiled Monday included a change to the way the federal tax code handles "carried interest," a provision allowing investors to pay tax on some income at the lower capital-gains rate rather than the standard rate for earned income. Among those who take frequent advantage of the provision are managers of hedge funds and private equity firms. Supporters say the provision is an incentive for better performance by investment managers, but critics say it's a loophole for the super-rich.

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The change requires any asset to be held for three years before a taxpayer could claim the carried-interest provision. The change, Brady said in a Monday morning CNBC interview, would "make sure it really is focused on those long-term, traditional real estate partnerships" rather than hedge funds. But it would stop well short of the complete repeal long advocated by Democrats who argue that carried interest allows investors to recast ordinary income earned for services rendered as investment income subject to a lower rate.

The proposed change comes as Democrats criticize the bill as a giveaway to the wealthy — a charge Republicans deny — and several nonpartisan analyses have suggested the very wealthy would enjoy an outsize share of the measure's proposed $1.5 trillion in tax cuts over a decade.

Brady rebutted recent studies, including from the Joint Committee on Taxation, that suggest that the GOP tax bill is heavily tilted in favor of businesses and the wealthy. According to the JCT's analysis, more than two-thirds of the $1.5 trillion tax cut would go to businesses and wealthy families who would avoid the estate tax.

"We want a dramatically more pro-growth tax code where our companies, whether they are local or global, can compete and win anywhere in the world, including here at home," Brady said, adding that the rewrite was "about flattering the tax code, making it understandable and fair."

The amendment unveiled Monday also appeared to address concerns from multinational firms who opposed a new 20 percent tax on certain transactions between corporate affiliates meant to discourage those firms from shifting profits to lower-taxed countries. It also reduced the reach of a new 1.4 percent tax on large university endowments, applying it only to institutions with assets of $250,000 per enrolled student or more, vs. the $100,000 threshold in the initial bill. Also protected is the current $5,000 per year exclusion for employer-provided dependent-care savings accounts.

Brady introduced the bill last week as part of his party's effort to make the biggest changes to the U.S. tax code since the Reagan administration. The Ways and Means markup session could stretch into Thursday as committee Republicans and Democrats propose, debate and vote on amendments to the measure. Republican leaders hope to pass their bill through the House by Thanksgiving.

The debate turned heated at times Monday, with several Democrats raising their voices to accuse Republicans of rushing the process and misrepresenting the effects of the bill.

"Why are you doing this?" Rep. Sander M. Levin (D-Mich.) shouted to Brady at one point. "You are desperately looking for something to pass."

Other changes that Republican tax writers discussed Sunday in a closed-door meeting were not included — such as an increase in the bill's proposed $500,000 limit on the mortgage interest deduction or the preservation of existing tax incentives for adoptive families.

Rep. Diane Black (R-Tenn.), a Ways and Means member who is pushing to maintain the adoption incentives, said discussions were continuing. "We want to make sure that it really, truly takes care of those children that are most in need," she said.

GOP lawmakers also did not change the treatment of "pass-through" businesses — firms where earnings are passed to its owners to be taxed as individual income. Lawmakers are exploring how to expand eligibility for a new 25 percent rate on that income, in part to address the concerns of the National Federation of Independent Business, a lobbying group. But any expansion could explode the cost of a provision already estimated to cost roughly $450 billion over the coming decade.

The NFIB said last week it would oppose the initial version of the bill because it "leaves too many small businesses behind" by leaving them ineligible for the lower rate. "We believe that tax reform should provide substantial relief to all small businesses, so they can reinvest their money, grow, and create jobs," the group said.

And serious discussion remains about repealing the Affordable Care Act's individual mandate, which could give the tax writers room to make these or other costly changes without exceeding a $1.5 trillion limit on the total cost of the bill over the coming decade. Repealing the mandate would mean fewer Americans would purchase insurance using federal subsidies, leading to less government spending.

Although the Congressional Budget Office estimated last year that a repeal would have a $416 billion positive deficit impact, updates to the nonpartisan scorekeeper's model have significantly reduced that figure, according to GOP officials. One of the officials said Monday that the new analysis will not be available until later in the week.

The Senate Finance Committee is expected to unveil its version of a tax bill Thursday once the House committee's proceedings end, according to multiple aides familiar with the plans, setting up its own markup next week.

Damian Paletta contributed to this report.