House Republicans survived the first skirmish on their tax cut bill Thursday, pushing a $1.5 trillion plan through committee after last-minute changes to appease conservatives by restoring small but symbolic tax breaks such as the adoption credit.

The 24-16 party-line vote in the Ways and Means Committee sets up a vote next week in the full House, where Republican leaders will see whether they have been able to tweak their bill enough to win over wary blue state Republicans while keeping conservatives on board.

“After years of work, dozens of hearings and multiple frameworks, we are one step closer to delivering true tax reform to the American people,” said committee Chairman Kevin Brady, Texas Republican.

The committee voted on the fourth day of debate after Republicans batted back a number of attempts by Democrats to delay or scuttle tax cuts.

The bill that emerged looked largely similar to the one Mr. Brady announced last week, though Republican leaders made significant changes to try to gain budget space and mollify antsy Republicans.

In one major change Thursday, Mr. Brady agreed to restore the adoption tax credit, a favorite of pro-life conservatives who say that while not much financially, it was big symbolically. The credit of up to $13,570 helps adoptive parents cover expenses for completing the process.

Rep. Diane Black, Tennessee Republican, thanked Mr. Brady for preserving the credit, saying it aids families who have room in their hearts and homes but not always in their budgets.

“We want to make certain that the tax code works for families who are willing to open up their homes to adoption and not against them,” she said.

Mr. Brady also announced a lower rate for small businesses earning less than $75,000 a year, dropping their tax from 12 percent to 9 percent. Such changes were enough to win support of the National Federation of Independent Business, a crucial interest group for Republicans that had been cool on the initial plan.

“We are very grateful to Chairman Brady for listening to our concerns and working with NFIB to ensure that tax reform benefits the greatest possible number of American small-business owners,” said NFIB President and CEO Juanita Duggan.

The crux of the tax plan remains the same, however: Corporate income rates are cut from 35 percent to 20 percent, with a new 25 percent rate for companies that file taxes as individuals; the standard deduction is nearly doubled; the estate tax is eliminated; and the existing seven tax brackets are compressed to four.

The legislation also raises the amount parents can save with the child tax credit and creates a credit for other dependents such as elderly parents.

But a number of special breaks taxpayers have relied on, such as the mortgage interest deduction, medical expense deduction or student loan help, are trimmed or axed altogether.

The goal, Republican leaders said, was to try to cut taxes for the most people while not bursting the deficit beyond the $1.5 trillion limit they have allowed themselves.

Rep. Richard E. Neal of Massachusetts, the ranking Democrat on the committee, said Republicans were trying to “put a size 12 foot in a size 7 shoe” in getting the math to work.

“It’s hard to do under the best of circumstances,” Mr. Neal said. “It gets more raw every day that falls off the calendar as you get to the election.”

Democrats said their sweeping election victories this week, particularly in purple Virginia, are signals that Republicans should slow their push.

“If they think that this is the bill that they must pass in order to stay in power, they have it all wrong. The public is hearing the truth. The public is paying attention,” said House Minority Leader Nancy Pelosi, California Democrat.

But even before this week’s elections, Republicans said they needed to notch a win on tax reform to give voters a reason to turn out next year, especially after their Obamacare repeal effort stalled out.

“This is something we ran on,” said House Speaker Paul D. Ryan, Wisconsin Republican. “I fundamentally believe … when we do this — make good on our word, make good on our promise, make people’s lives better — we’re going to be just fine politically.”

The test when the bill reaches the floor next week will be whether it scares away too many blue state and suburban Republicans. Democrats say those constituents will be hit hard by the plan to impose a $10,000 limit on deductions for property taxes, and to eliminate deductions for state and local income taxes, which are generally higher in blue states.

If the bill passes the House, it will ultimately have to be reconciled with a Senate version, either in a bicameral conference committee — which Mr. Ryan predicted Thursday — or with both chambers simply approving identical plans.

Senate Republicans rolled out their own plan on Thursday that contained notable differences from the House plan. It included a full repeal of the state and local tax deduction and a one-year phase-in for lowering the corporate tax rate from 35 percent to 20 percent.

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