WASHINGTON — Senate Republican leaders on Monday faced rising odds that they will have to radically alter their plan to overhaul the tax code, as they struggled to contain defections on the eve of a key vote.

Sen. Ron Johnson, R-Wis., vowed Monday to vote against the package during a Senate Budget Committee meeting Tuesday unless his concerns are addressed. With 12 Republicans and 11 Democrats on the panel, his opposition could prevent – or at least delay – the legislation from going to the Senate floor this week as Republican leaders had planned.

Johnson wants more tax cuts for millions of companies, known as “pass-throughs,” that effectively pay their taxes through the individual tax code. Johnson originally came out with his concerns about the bill nearly two weeks ago while expressing hope that sufficient changes would be made.

But on Monday, he said he was not yet satisfied, an indication of how difficult the bill’s math is. “If we develop a fix prior to committee, I’ll probably support it. But if we don’t, I’ll vote against it,” Johnson told reporters in Wisconsin.

If the bill fails to advance through the Budget Committee Tuesday, party leaders will be forced to either enter difficult new negotiations to amend the bill or possibly scrap the Senate version in favor of a far different tax bill passed by the House this month.

Either of those actions would delay the process, threatening President Donald Trump’s goal of passing tax legislation this year and colliding with another fragile effort to avert a government shutdown next month.

Adequately addressing Johnson’s concerns could add hundreds of billions of dollars to the bill’s effect on the federal debt, which in turn could draw steep opposition from other Republicans.

Leaders would then have to address those criticisms before the full Senate could vote on the legislation, given the party’s narrow 52-48 margin in the chamber.

Sens. James Lankford, R-Okla., Bob Corker, R-Tenn., and Jerry Moran, R-Kan., were pushing Monday for strict assurances that the tax plan won’t add to the debt after a decade, potentially putting swing-vote lawmakers on a collision course.

They were discussing a form of automatic tax increase in the form of higher rates or eliminating deductions if the law is on target to add to the deficit a decade from now. The Senate has voted to allow the plan to add $1.5 trillion to the deficit over the next 10 years but not beyond.

“It is very important to me to know we aren’t increasing deficits,” said Corker, who also sits on the Senate Budget Committee. “This is important to us to be worked out in advance” of the committee’s vote, he added.

Senate leaders, while hopeful that they could find solutions to appease concerned senators, expressed frustration Monday that the effort was bogging down.

Sen. Roy Blunt, R-Mo., the vice chairman of the Senate Republican Conference, said the issue raised by Johnson was “worth talking about” and that leaders are “trying to find a way forward that does part of what he wants.”

But, he added, “I think senators should expect to be heard, and then have to look at the final bill as opposed to current tax law and decide how they’re going to vote.”

In addition to Johnson, Sen. Steve Daines, R-Mont., has raised concerns about how “pass-throughs” are treated under the plan.

The two senators are demanding that the companies are afforded the same tax treatment as large corporations, which would see their tax rate fall from 35 percent to 20 percent in the legislation. They propose paying for better treatment by eliminating the state and local tax deduction for businesses, as the Senate bill does for individuals.

“We need to make sure we’re taking care of the main-street businesses in this country, and not just the large corporations,” Daines said. “The vast majority of private-sector jobs in this country come from main-street businesses, not from corporations.”

There are now about 10 Republican lawmakers seeking changes to the tax plan, although it is unclear how many would oppose the bill if their demands aren’t met. Republicans have only two votes to spare if they want to pass their proposal because it is not expected to attract Democratic support.

While Johnson’s demands have rattled the White House for more than a week, the growing headache for Republican leaders is coming from Lankford, Corker and Moran.

That’s because the tax cut package would add $1.4 trillion to $1.5 trillion to the debt over 10 years, according to budget estimates, and it could add hundreds of billions of dollars more if temporary tax cuts in the package are extended.

The government has more than $20 trillion in outstanding debt, and Lankford said he is concerned about adding even more. Many Republicans were staunch deficit hawks during the Obama administration, but they have changed their approach after the election of Trump.

“What if this doesn’t work?” Lankford asked Monday, referring to tax cuts in the Senate plan. “What changes might be needed in the tax code in the days ahead to be able to adjust in what scenario? So if the revenue’s not coming in, should the rates change? All of those are in conversation.”

Sen. John Cornyn, R-Texas, the No. 2 Republican in the Senate, said others have raised concerns about the possibility of adding a trigger, an automatic tax increase should the proposal fall short of generating enough revenue, because it could create uncertainty about what future tax rates might be.

“That’s one of the policy objections that I’ve heard,” he said. “People say that at a time when you’re expecting economic growth as a result of the tax cuts, that you create a mechanism that makes it hard to predict what taxes are going to be. So nobody said it’s going to be easy.”

Johnson and Daines are focused on firms such as partnerships, limited-liability companies and sole proprietorships that pass through their income to investors and partners. There are millions of these firms, which can range from small businesses to National Football League teams and entities such as the Trump Organization.

The Senate bill would allow these companies to take a temporary credit of up to 17.4 percent of their income and deduct that from their taxable income. To entice Johnson and Daines, Republican leaders have suggested they could expand the deduction to up to 20 percent of their income. But Johnson has suggested even that might not be enough.

Other senators were presenting different demands. Sen. Susan Collins, R-Maine, has said she wants the Senate bill changed in a way that allows Americans to deduct their local property taxes from their federal taxable income. A tax-cut bill that passed the House allowed Americans to deduct up to $10,000 in property taxes from their income, but the Senate bill doesn’t include such a provision.

Sen. Jeff Flake, R-Ariz., has expressed concerns about how the tax bill would add to the debt, and he has said he is pushing for changes that would account for the cost of extending tax breaks that are only scheduled to last for several years.

Sen. Lisa Murkowski, R-Alaska, and Sen. John McCain, R-Ariz., have issued generally supportive statements of the tax plan but have also said they are undecided. Both Murkowski and McCain have shown a willingness in the past to buck the Trump administration in pivotal situations, opposing Trump’s earlier effort to repeal the Affordable Care Act.

Sen. Marco Rubio, R-Fla., meanwhile, wants to expand the child tax credit, a change that also could add to the government’s debt.

If the Senate passes its tax measure by the end of this week, Republican leaders would need to reconcile differences between their tax bill and the one that previously passed the House.

That could happen either in a formal “conference” process, or the House could simply vote to approve the Senate bill in its entirety, sending the bill to Trump so that he can sign it into law.

Senate Finance Committee Chairman Orrin Hatch, R-Utah, met with Trump and several other GOP senators Monday as they prepared for the final push and was asked if he thought a final bill would be signed into law by Christmas.

“I hope so,” Hatch said.