Senate Finance Committee Chairman Orrin Hatch (R-Utah), center, and Sens. John Cornyn (R-Tex.), right, and Patrick Toomey (R-Pa.), left, walk from the West Wing to speak to reporters after a meeting with President Trump on Monday. (Jabin Botsford/The Washington Post)

Senate Republican leaders on Monday faced rising odds they would have to radically alter their plan to overhaul the tax code, as a spate of defections threatened to upend plans to pass the bill as soon as this week.

Sen. Ron Johnson (R-Wis.) vowed Monday to vote against the package during a Senate Budget Committee meeting Tuesday unless his concerns were addressed. With 12 Republicans and 11 Democrats on the panel, his opposition could derail GOP leaders' plans to bring the tax bill to the Senate floor on Wednesday.

Johnson wants more tax cuts for companies, known as "pass-throughs," that effectively pay their taxes through the individual tax code. Johnson originally aired 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 the bill's difficult math. "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 on Tuesday, party leaders will be forced either to enter difficult new negotiations to accommodate Johnson or circumvent the Budget Committee — a move that could alienate senators concerned about the legislative process.

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

Addressing Johnson's concerns could add hundreds of billions of dollars to the federal budget deficit, requiring offsetting changes elsewhere in the bill that could generate opposition from other Republicans.

Already, Sens. James Lankford (R-Okla.), Bob Corker (R-Tenn.) and Jerry Moran (R-Kan.) are pushing for strict assurances that the tax plan won't add to the national 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.

Leaders must address the criticism before the full Senate can vote on the legislation, given the party's narrow 52-t0-48 margin in the chamber. Corker, who also sits on the Senate Budget Committee, said he wanted the fiscal concerns "to be worked out in advance" of the panel's vote Tuesday. "It is very important to me to know we aren't increasing deficits," he said.

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 — partnerships, limited-liability companies and sole proprietorships — 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 lower rates by eliminating the state and local tax deduction for businesses, as the Senate bill does for individuals.

The Senate bill would allow the owners of these companies, in some circumstances, to deduct 17.4 percent of their earnings from those firms from their taxable income. To entice Johnson and Daines, GOP leaders have suggested they could expand the deduction to up to 20 percent of the qualified income. But Johnson suggested even that might not be enough.

"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 GOP 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 GOP 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-Tex.), the No. 2 Republican in the Senate, said others have raised concerns about the possibility of adding an automatic tax hike if the plan adds more to the deficit than anticipated, since 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."

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.

Sen. Jeff Flake (R-Ariz.) 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, out of concern that Congress is undercounting the true cost of the proposal.

Sen. Lisa Murkowski (R-Alaska) and Sen. John McCain (R-Ariz.), who earlier showed they'd buck the party by opposing a repeal of the Affordable Care Act, have issued generally supportive statements of the tax plan but have also said they are undecided.

Sen. Marco Rubio (R-Fla.) 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, GOP 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 G. 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.

John Wagner and Paul Kane contributed to this report.