According to the Congressional Budget Office, getting rid of the Affordable Care Act’s mandate that most people have health coverage would reduce federal deficits by a total of $416 billion by 2026, mainly because fewer people would be enrolled in Medicaid and in private health plans subsidized by the government. The same analysis said that repealing the individual mandate would cause a substantial increase in the number of people without health insurance.

While Republican congressional leaders originally hoped that repealing the health law — and its taxes — would help make their tax overhaul easier, most have decided that injecting the toxic politics of health care into the tax effort could imperil their chances of getting a bill passed. Senator Orrin G. Hatch, Republican of Utah and the chairman of the Finance Committee, said on Wednesday that health care should be kept out of the tax bill. Mr. Brady has also expressed concerns about marrying the two.

The Republicans’ plan is also likely to include a major concession to social conservatives: the repeal of a law known as the Johnson Amendment, which prohibits tax-exempt entities like churches from participating in political campaigns. The law, which has been in place since 1954, has been a source of contention for many Christian conservatives who have argued that it restricts the rights of pastors and other religious leaders to speak freely. Mr. Trump has repeatedly vowed to push to eliminate the law.

At a meeting that Speaker Paul D. Ryan of Wisconsin held with conservative leaders on Tuesday, he indicated that a repeal would be in the House plan, according to two people in attendance.

As the Ways and Means Committee scurried to finish the bill by Thursday, Representative Patrick T. McHenry, Republican of North Carolina and the chief deputy whip, played down the significance of the one-day delay, while adding that Republicans were still on pace to move quickly.

“Arbitrary deadlines do not work,” he said. “We saw that with health care. We’re not going to allow the idea of rolling out on a Wednesday rather than a Thursday determine something as substantive and as important as tax reform.”

Representative Tom MacArthur, Republican of New Jersey, said a plan was taking shape to resolve the conflict over the state and local tax deduction, which has threatened to derail the bill. Republican lawmakers from high-tax states have been adamant that the deduction remain largely intact or at least in some form that is acceptable to constituents. Mr. MacArthur said the plan would allow property taxes to be deducted, with a cap that he said needed to be higher than what had been sketched out.