House Republican leaders made a frantic attempt Wednesday to keep their aggressive tax overhaul effort on schedule, working to win over members who have balked at a proposal to ditch a key income tax deduction.

The House is scheduled to cast a critical budget vote Thursday which would set out key parameters for the tax bill and pave the way for Republicans to pass it without Democratic cooperation. But some of the Republicans concerned about the effort to eliminate or limit the existing deduction for state and local taxes have threatened to vote no, potentially blocking the legislation's progress.

Speaker Paul D. Ryan (R-Wis.) said this week that he plans to pass the tax bill through the House by Thanksgiving, and any delay in the budget vote could upset that timetable.

At least four GOP lawmakers from high-tax states said Tuesday that they intended to vote against the budget unless a deal is in place to at least partially preserve the state- and local-tax deduction, also known as "SALT."

All were dismayed by language included in the latest version of the budget that refers to "reducing federal deductions, such as the state and local tax deduction which disproportionately favors high-income individuals." They argue that many middle-class households in high-cost-of-living areas take advantage of the deduction.

House Speaker Paul D. Ryan (R-Wis.) talks to reporters after the weekly House Republican Conference meeting at the U.S. Capitol on Oct. 24, in Washington, D.C. Ryan and the GOP leadership said that tax cuts and reforms are their priority and they hope to get legislation out of the House by the Thanksgiving holiday. (Chip Somodevilla/Getty Images)

"That language shouldn't have been added to the Senate budget," said Rep. Lee Zeldin (R-N.Y.). "Unless I get more concrete information on a reasonable agreement, then I will be a no on Thursday."

House Ways and Means Committee Chairman Kevin Brady (R-Tex.) on Wednesday evening said GOP leaders will "take our time with those members, because we want to see people keep more of their earnings, regardless of where they live, including in high-tax states." He said he is confident Republicans have the support necessary to pass their spending blueprint, "because this budget vote is about allowing pro-growth tax reform to occur. It isn't the tax bill."

House GOP leaders are planning to huddle with the blue-state Republicans on the issue following the budget vote Thursday, a leadership source said.

The committees crafting the tax bill are counting on the elimination of the deduction to generate hundreds of millions of dollars in revenue to offset rate cuts and other provisions in the tax bill.

Among the options under discussion are allowing taxpayers to deduct only their property taxes, not income or sales taxes; phasing out the deduction for higher-income taxpayers; or replacing the deduction with a tax credit that could also be phased out for high earners.

"This is a big issue, and it has to be resolved," said Rep. Tom MacArthur (R-N.J.). "Tax reform is good for the country. It's just not good for the country when it's on the back of six states. That's the problem."

Ryan acknowledged at an event hosted by Reuters on Wednesday that a full repeal of the SALT deduction was unlikely and that a compromise would have to be reached.

"I think there's a way of addressing the concerns that our members have from middle-income taxpayers in those states so that they are net winners in tax reform as well," he said.

Rep. Tom Reed (R-N.Y.), a member of the tax-writing Ways and Means Committee who has been negotiating a compromise, said he thinks a deal with House leaders is in reach.

"They recognize the serious nature of the problem that needs to be addressed, and that is where I think the total repeal of the state and local tax deduction, in my opinion, is off the table and going in the right direction," he said. "Obviously, if we had a preference, we'd love to keep it, but I think the reality of a good-faith compromise is where I think we will land."

Reed said that a final deal may not materialize before the budget vote, but that significant progress toward a deal could win over balking members.

"Because [leaders are] acting in good faith, I expect members to act in good faith," he said. "If that's where we get — to where we have, not a deal, but a solution in concept — that will probably be enough to move us to the next level."

The House GOP's chief vote counter said things were on track for the budget's passage Thursday but acknowledged that some members still needed convincing from GOP leaders. Multiple Republican leadership aides said they expected the vote to be close but ultimately successful.

"We're gonna get this thing done," House Majority Whip Steve Scalise (R-La.) said in a brief interview. "They're working really hard. We want to work with them to find a solution."

There were signs Wednesday that the SALT deduction proponents might be splintering in their effort to force action before the budget vote. Some of those who had threatened earlier in the week to vote against the budget absent a deal stepped back from those threats, and at least two New York Republicans, Reed and Rep. Chris Collins, said they would vote for the budget. A meeting of the balking members set for Wednesday evening in Ryan's office to discuss options for addressing the deduction was canceled late in the day amid growing confidence that House leaders had secured the votes.

"I believe there are Republicans who want to vote no who will vote yes if their vote is needed because we all know we have to get to tax reform, and there's only one way to get there," Collins said. "So with the urgency of that, I think we do get there."

Rep. Doug LaMalfa (R-Calif.) said that while he still had questions about the handling of the SALT deduction, he would not vote against the budget. "I don't think that's the way to do it," he said.

Democrats, meanwhile, warned of dire political repercussions for Republicans in states where the SALT deduction is popular.

"If you live in any of the states where there is a state and local tax, you are going to pay a lot more taxes, and your Republican member is the person who is going to facilitate that or not," House Minority Leader Nancy Pelosi (D-Calif.) said in an interview Tuesday. "And one of the things we are doing now is to make sure that people know what this means to them."

"It would be a tremendous advantage to go after those people in their districts on that," she added. "But we don't want to do that. We want to protect those people from that action. That's our priority. Let's just defeat that."

Michael Scherer contributed to this report.