Senate and House Republicans have struck an “agreement in principle” on a sweeping tax-cut bill that if passed would be the first major piece of legislation signed by President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE.

Senate Finance Committee Chairman Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah) told reporters about noon Wednesday of the deal between Senate and House negotiators on taxes.

“We’re going to talk to our members of conference about it at noon,” said Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas).

Senate Republican leaders say they have the votes to pass the legislation next week.

“I’m confident we’ll pass the bill next week,” Cornyn said. “Earlier is better.”

GOP sources familiar with the conference committee talks said negotiators are now just cleaning up some of the details on paying for last-minute changes to the bill, which would lower the top individual tax rate to 37 percent and set the corporate tax rate at 21 percent, according to a person briefed on the package.

That's slightly higher than the 20 percent corporate rate initially favored by President Trump, a rate that outside groups have lobbied to keep in the package.

House conservatives said they didn't like the bump in the corporate rate. But with a tax victory so close, they said the tweak would not be a deal breaker.

"We don't like it; it causes some consternation. I am concerned about the business rate," Rep. Mark Walker Bradley (Mark) Mark WalkerMike Johnson to run for vice chairman of House GOP conference The Hill's Morning Report - Sponsored by National Industries for the Blind - Woodward book revelations rock Washington The Hill's 12:30 Report — Presented by Facebook — Trump, Biden duel in final stretch | Vaccine trial on pause after recipient's 'potentially unexplained illness' | Biden visits Michigan | Trump campaign has 18 events in 11 states planned in the next week MORE (R-N.C.), chairman of the conservative 155-member Republican Study Committee caucus, told The Hill on Wednesday. "When these business communities are looking to build, every percentage point is a major factor in this, so we want to be careful in going in that direction.

"But it's not a deal breaker," he added.

The bill would also cap the popular mortgage interest deduction at $750,000, a midpoint compromise between the Senate and House bills.

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Senate Republicans met midday Wednesday in the Mike Mansfield Room off the chamber floor to go over details of the agreement.

Senators left the room feeling positive.

“I don’t think there’s going to be any doubt this is going to be a very pro-growth tax package,” said Sen. Ron Johnson Ronald (Ron) Harold Johnson CIA found Putin 'probably directing' campaign against Biden: report This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report MORE (R-Wis.).

“There’s been a real healthy melding of House provisions and Senate provisions. My guess is it’s going to have broad support,” he added.

Several lawmakers warned, however, that the package is not yet final.

Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) will brief House Republicans at 3 p.m. in the Capitol.

Lawmakers are rushing to get the bill done before the Christmas holiday.

Cornyn said he expects the Senate to hold an initial procedural vote Monday and a final vote Tuesday.

The deal will have been struck before the first official House-Senate conference on the bill, which was held Wednesday afternoon.

Democrats have generally been locked out of the process as Republicans have sought to finish their legislation before the end of the year.

The legislation will repeal the federal mandate requiring people to buy insurance — a core piece of ObamaCare.

The bill also would give some relief to people in high-tax areas by allowing them to deduct up to $10,000 in state and local property or income taxes.

The deduction for pass-through companies will be set at 20 percent, somewhat lower than the 23 percent included in the Senate-passed bill. But that will be offset by lowering the top individual income rate to 37 percent from its current level of 39.6 percent.

Johnson said the pass-through rate will include trusts and establish an effective top tax rate of 29.6 percent.

Negotiators also knocked out a House-passed provision that would eliminate the student loan interest deduction. They also killed a provision that would tax tuition waivers received by some grad students.

“Folks who are in grad school will feel pretty good about the final result,” said Sen. Mike Rounds Marion (Mike) Michael RoundsSenate GOP sees early Supreme Court vote as political booster shot Chamber of Commerce endorses McSally for reelection Senate GOP eyes early exit MORE (R-S.D.).

Meanwhile, a provision to set a corporate alternative minimum tax — which would have raised $40 billion over 10 years — has been stripped out.

Several Senate Republicans are not happy about the proposal to lower the top individual rate to 37 percent but they acknowledged they needed to give some ground to House negotiators.

“It would not have been one of my high priorities, there would have been other priorities for me but we’re dealing with the House. We all know we’re not going to get everything we want,” Rounds said.

Sens. Susan Collins Susan Margaret CollinsSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-Maine) and Marco Rubio Marco Antonio RubioOvernight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers Democrats step up hardball tactics as Supreme Court fight heats up Press: Notorious RBG vs Notorious GOP MORE (R-Fla.) also balked at lowering the top individual rate to 37 percent, but it’s unlikely that the change will cause them to oppose the bill.

“I’m going to wait and look at the entire conference report once it comes out,” Collins said.

The Trump administration and GOP leaders have helped win over Collins by promising to pass legislation to shore up the individual health insurance markets.

Vice President Pence assured Collins of the commitment to pass legislation authorizing the payment of subsidies to insurance companies and funding states to set up high-risk reinsurance pools to keep premiums in check.

“I had a very good discussion with the vice president yesterday about that issue and I feel certain the agreement that I negotiated will be kept — this year,” she said.

Jordain Carney contributed.

Updated: 1:22 p.m.