WASHINGTON - The Republican effort to rewrite the tax code surged forward Tuesday as a Senate panel approved the measure and several wavering lawmakers signaled they are leaning toward backing the bill.

The Senate Budget Committee voted 12-11 to send the $1.4 trillion tax package to the Senate floor for a vote later this week. That margin was in doubt until the votes were cast because two Republicans, Sens. Bob Corker of Tennessee and Ron Johnson of Wisconsin, had threatened to oppose it.

But Corker said he had reached an agreement with GOP leaders to add a mechanism that would limit the tax plan's impact on the debt, and Johnson said he would vote to back the bill in the committee to keep the process moving.

"I was able to work out something that is fairly satisfying to me," Corker said.

His support for the bill now appears far more certain, while Johnson's stance remains in doubt. Johnson did not say his concerns about the tax package had been resolved, and he has a chilly relationship with Senate Majority Leader Mitch McConnell (R., Ky.).

The budget committee vote came just minutes after President Trump met with Senate Republicans on Capitol Hill and offered numerous concessions to win over skeptical members. Importantly, he promised Sen. Susan Collins (R., Maine) that he would support continuing federal subsidies to help lower-income Americans afford health coverage if the tax bill repealed part of the Affordable Care Act.

He also told senators that he supported changing the bill in a way that would allow Americans to deduct up to $10,000 in their personal property taxes.

That concession could help win over other GOP members, though it could drive up the size of the tax package unless Republicans find ways to offset the lost revenue.

Collins said she is "still working on a bunch of issues, but I'm encouraged by the response to my proposals to the property-tax deduction and on mitigating the impact of the individual mandate."

The House has already passed its version of the tax plan. If Senate Republicans can unite behind their bill, the House and Senate would need to pass matching versions before the measure could be signed into law by Trump.

There are major differences between the two pieces of legislation, but Republicans appear motivated to cut a deal before the end of the year, given their broad goals of cutting taxes and notching a legislative victory at the end of an uneven year.

The Senate tax bill would slash the corporate tax rate from 35 percent to 20 percent starting in 2019 and temporarily lower the tax rates paid by individuals and families through 2025. It would also repeal a provision of the Affordable Care Act that sets up penalties if Americans don't have health insurance, a central plank of the Obama administration's signature health care law.

No official analysis has been released by the Treasury Department or the nonpartisan congressional Joint Committee on Taxation to support the GOP claims that economic growth generated by the tax plan would make up for the major revenue losses.

Corker, a self-described "deficit hawk," said he did not expect to see any such analysis this week, prompting his push for the fiscal trigger provision.

Johnson's opposition, meanwhile, is based on his complaints that the bill would not sufficiently lower taxes for millions of businesses that are effectively taxed through the individual income tax code. These businesses, known as "pass throughs," would receive temporary tax cuts that expire in 2025, unlike the tax cuts for corporations, which would be made permanent.

Republican leaders were scrambling Tuesday to address the myriad concerns, an effort that appeared to be working.

Republicans control 52 votes in the 100-seat Senate, and they can afford to lose the support of only two members if they want the measure to pass. Democrats have signaled they are united in their opposition to the tax bill.

Various estimates show the tax plan disproportionately benefits corporations and the wealthy, with many middle class Americans seeing their taxes increase over time. Republicans have said they will not allow the middle class to see a tax increase and would change the bill if needed, but it has left an opening for Democrats to attack the plan.

"This legislation is a disastrous and unfair piece of legislation that gives huge tax breaks to the people who need it the least, the very, very wealthy," said Sen. Bernie Sanders (I., Vt.).