Top Republicans batted aside complaints that they were trying to buy support for their tax cut bill in the final hours before a vote Tuesday and were increasingly confident that they would deliver a victory to President Trump this week.

Sen. Susan M. Collins of Maine, the least-conservative Republican in the chamber, announced Monday that she would support the bill, giving an extra boost to the legislation.

She was the latest to swing behind the 694-page bill, which promises $1.5 trillion in tax cuts, a repeal of the Obamacare individual mandate and a repeal of the prohibition on drilling for oil in key parts of Alaska.

“This legislation will provide tax relief to working families, encourage the creation of jobs right here in America and spur economic growth that will benefit all Americans,” Ms. Collins said in a floor speech.

She joins Sens. Marco Rubio of Florida, Mike Lee of Utah and Bob Corker of Tennessee, all of whom had expressed reservations but now say they back the bill.

Mr. Corker, the lone Senate Republican to vote against a previous version of the tax cut bill, became the subject of intense scrutiny over the weekend when a press report said he would benefit from a change to a small-business investment provision.

Democrats dubbed it the “Corker kickback” and accused the Republican of vote-buying in the same way that Democrats were accused of vote-buying on Obamacare seven years ago.

“Republicans are racing to pass the bill before the public can discover all the giveaways, but the American people already recognize the tax scam for the daylight robbery it is,” said House Minority Leader Nancy Pelosi, California Democrat.

But Mr. Corker’s office said he had nothing to do with the provision and was unaware of it when he made his stance known last week.

Republican leaders declared the entire issue a farce, saying the House version of tax cuts had long envisioned the provision, and it wasn’t a last-minute buy-off.

Sen. Orrin G. Hatch, Utah Republican and chairman of the Senate Finance Committee, called the reports accusing Mr. Corker of taking a buy-off “an irresponsible and partisan assertion that is belied by the facts.”

Sen. John Cornyn, Texas Republican, said the weekend reports attacking Mr. Corker were part of an effort to poison fast-moving action.

“What the whole purpose of this exercise was, this false and invented story, is to undermine public confidence in this tax reform package that we will pass perhaps as early as tomorrow and be signed by the president before Christmas,” said Mr. Cornyn, the chamber’s second-ranking Republican.

Republicans are racing to pass the bill by Christmas because quick action means tax cuts can start sooner next year and because Republican forces are slated to be reduced in 2018.

Democrat Doug Jones’ victory in Alabama’s special election last week will cut the Republican majority from 52 to 51 seats, leaving them even less margin for negotiations.

Republicans are also grappling with scheduling. Sen. John McCain, the Arizona Republican who is battling brain cancer, will be absent this week as he recovers from treatment.

House Republican leaders have scheduled a Tuesday vote on the package, and Mr. Cornyn said the Senate would take up the measure right after the House vote, with final passage expected either late Tuesday or early Wednesday.

“We will get it on the president’s desk for him to sign into law before Christmas, as we pledged,” Mr. Cornyn said.

Budget analysts said the latest version of the bill, released late Friday, was riddled with gimmicks. They predicted deficits topping $2 trillion if the gimmicks are removed.

Under those gimmicks, some tax cuts are delayed, while the tax rate cuts for individuals are ended early, keeping the cost of the bill within the $1.5 trillion level set by the 2018 budget.

Most Americans will receive tax cuts next year under the bill, but thanks to the phaseouts, a majority would see tax increases in 2027, according to the Tax Policy Center’s latest analysis.

But the bill maintains the general progressive bent of the tax code, with the wealthy still footing the vast majority of the tax bill next year. The top 20 percent of taxpayers will pay 65 percent of all taxes, and the top 5 percent alone will account for 50 percent.

The $1.5 trillion plan cuts the corporate tax rate from 35 percent to 21 percent and trims individual rates, dropping the top individual rate from 39.6 percent to 37 percent.

The new benefits for “pass-through” companies that file their taxes as individuals are meant to provide some measure of parity with larger corporations, which will end up with a significantly lower rate than many small businesses.

The plan also eliminates various exemptions and deductions while expanding others, including the child tax credit, which was a change demanded by Mr. Lee and Mr. Rubio.

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