Many of the last-minute changes were included to help convince a handful of holdout Republican senators, including Susan Collins of Maine and Ron Johnson of Wisconsin, to throw their support behind the legislation. Others were included for reasons that left many Democrats crying foul.
One such change, added by Senator Patrick J. Toomey, Republican of Pennsylvania, was an exemption from the proposed excise tax on university endowments. Democrats said that the amendment would benefit only Hillsdale College, a Christian liberal arts school in Michigan with ties to the conservative Club for Growth and Betsy DeVos, the education secretary.
In a heated exchange, Ms. McCaskill accused Mr. Toomey of crafting an amendment that was “a very limited provision written for a very special person,” a reference to Ms. DeVos. The adjusted language would provide a federal funding exemption that would apply to Hillsdale.
Mr. Toomey said that any school that rejected such federal funding would also be exempt from the tax. On Friday night, after discovering the provision, Democrats were trying to have it stricken from the bill by the Senate parliamentarian.
The haste with which the changes were made reflect the rapid-fire approach that Senate Republicans have taken as they try to score their first significant legislative victory before the year’s end.
Republicans have pitched the bill as a middle-class tax cut and the overhaul is intended to immediately cut taxes for about 70 percent of middle-class families. But it would raise them on millions of others, since the Senate plan eliminates some tax breaks like the deduction for state and local income taxes and phases out the individual tax cuts at the end of 2025.
Businesses fare far better, with the corporate tax rate cut to 20 percent from 35 percent and made permanent. It also offers a large tax break for the owners of small businesses and other companies that are not organized as traditional corporations, a provision that was sweetened in a last-minute deal to bring two wavering senators on board.
Democrats appeared to be opposing the tax bill as a bloc, saying it was meant to help the wealthy and not the middle class. With the Senate split 52 to 48, Republicans barely have votes to spare. But the bill’s imminent passage was made possible by a near-complete Republican embrace of the idea that about $1.5 trillion of tax cuts will pay for themselves, by producing enough economic growth and additional federal revenue to offset their costs to the Treasury.
That belief was contradicted by several studies, including one from Congress’s official economic scorekeeper, which Republicans dismissed as overly pessimistic.
Once the Senate version is passed as expected on Friday, the chambers will work quickly to resolve the differences between their bills and deliver a plan to President Trump’s desk, with the aim of delivery by Christmas.
Congressional leaders raced the bill through the House and the Senate in a month, with a crush of changes coming in the 11th hour as Senate leadership worked to address the concerns of a few lawmakers whose support was critical to passage. Several changes were included to satisfy Ms. Collins, including a provision that will allow taxpayers to deduct up to $10,000 in state and local property taxes paid and allowing lower-income individuals to claim the medical expense deduction.
In the late afternoon, Ms. Collins announced her support for the bill, citing those changes as well as a promise from Mr. McConnell that he would support two bipartisan bills meant to help stabilize individual insurance markets under the Affordable Care Act. Ms. Collins had expressed concern about a provision in the tax bill to repeal the act’s mandate that most Americans have insurance or pay a penalty.
Lawmakers also included a more generous tax break for companies organized as pass-through entities, a provision needed to win the support of Mr. Johnson and Senator Steve Daines of Montana.
And, in a bid to get Senator Jeff Flake of Arizona on board, leaders agreed to work on providing “fair and permanent protections” for the beneficiaries of an Obama-era effort that protects young undocumented immigrants from deportation, known as Deferred Action for Childhood Arrivals, or DACA, Mr. Flake said.
“There are no ironclad commitments — at this date we’re going have a bill — but I am confident,” Mr. Flake said. “I’ve always been convinced on DACA that the president’s instincts are better than the advice he’s getting.”
Mr. Flake, an outspoken critic of Mr. Trump, said he had spoken with Vice President Mike Pence about the issue. “We had a long conversation last night and today, and he committed to start working with me on this,” Mr. Flake said.
Mr. Flake also said he had won changes in a provision, which expires after five years, to allow companies to immediately deduct new investment expenses, which he called a “gimmick.”
The bill would also open up the Arctic National Wildlife Refuge in Alaska to oil and gas drilling, putting environmental activists on the brink of defeat in what has been a decades-long battle. Opening the wildlife refuge to energy exploration has been a goal of Senator Lisa Murkowski, Republican of Alaska.
Several of the changes, most notably the property tax break and the additional deduction for pass-through businesses, combined to add several hundred billion dollars to the cost of the bill. To offset them, party leaders scaled back some planned tax cuts and increased a new tax on assets held overseas by American multinational companies.
Most notably, they decided to maintain the alternative minimum tax on corporations and to trim the effects of the alternative minimum tax for high-earning individuals. Originally, the bill would have eliminated both those taxes entirely.
None of those changes were likely to improve the fiscal cost of the bill — in defiance of the concerns that several senators had raised about adding to future deficits.
Chief among those worried about the deficit was Senator Bob Corker, Republican of Tennessee, whose fears over the bill’s effect on the federal budget deficit created last-minute complications for Republican leaders on Thursday when he demanded changes to the bill.
Mr. Corker had pushed to scale back the tax cuts after a report from the congressional Joint Committee on Taxation that projected the bill would add $1 trillion to deficits over a decade, even after accounting for economic growth.
Republicans said Mr. Corker had angered colleagues and overplayed his hand in the wake of that analysis. Mr. Corker was alarmed by the projections. But many of his colleagues greeted them with distrust, both because they expected tax cuts to generate more robust economic growth than the forecasters projected and because they felt burned by unflattering analyses of their health care proposals issued this year by the Congressional Budget Office.
The joint committee sprinted to complete its analysis of the Senate bill before the vote, having failed to complete one of the House version before it was passed two weeks after its introduction. Still, Republicans wondered why the analysis arrived on Thursday, the day the Senate was originally scheduled to vote, a leadership aide said on Friday.
The timing and the scoring of the analysis generated a lot of suspicion, the aide said.
Mr. Corker pointed to the analysis to push for rolling back of some of the tax cuts after several years, to reduce the bill’s cost, but many of his colleagues revolted over that idea. Republican leaders decided on Thursday night to drop efforts to appease Mr. Corker and instead sweeten their offer to Mr. Daines and Mr. Johnson, by offering to allow pass-through owners to deduct 23 percent of their business income, up from 17.4 percent in the original bill.
Previously, the leaders had offered a deduction of 20 percent. The increase to 23 was enough to get both men on board.
“After weeks of fighting for Main Street businesses including Montana’s farmers and ranchers, I’ve decided to support the Senate tax cut bill, which provides significant tax relief for Main Street businesses,” Mr. Daines said in a statement Friday morning.
Mr. Johnson followed with his own pledge of support.
“I wanted more,” he said, “but I’m a reasonable human being.”
Mr. Johnson had helped give a scare to Republican leaders on Thursday, as he, Mr. Corker and Mr. Flake withheld their votes as Republicans were trying to kill a Democratic motion to relegate the bill back to a Senate panel.
“Senator Corker called me and said, ‘Why shouldn’t we vote for that one?’” Mr. Johnson recalled on Friday.
“There’s always parliamentary maneuvers, right?” he said. “So we didn’t vote.”
Recounting how the vote played out, Mr. Johnson said, “I was just kind of biding my time.” Eventually, he said, a Republican colleague, Rob Portman of Ohio, came over to see what could be done.
The deal to sweeten the tax break for pass-through businesses came together later that night, as Mr. Johnson, Mr. Daines and Senator Lindsey Graham of South Carolina met with Senator John Cornyn of Texas, the No. 2 Senate Republican, in his Capitol office to make a case to Senate leadership.
“There’s a lot of competing interests,” Mr. Johnson said, likening the bill to a Rubik’s Cube.
“I guess they put that Rubik’s Cube together,” he added.
While Ms. Collins publicly remained undecided on the bill over the past week, Republican leaders were confident they would bring her on board. She made her demands clear early in the process, and she actively negotiated with the leadership until the day of the vote.
Mr. Corker appeared to be the only member of his party set to vote against the bill.
Democrats warned on Friday that Republicans were making a political mistake with a bill that would increase taxes on some middle-class families.
“It’ll be a dramatic turning point in a downward spiral for the Republicans,” said Senator Chuck Schumer, Democrat of New York and the minority leader.
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