WASHINGTON — 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 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.

Four Republican lawmakers from the high-tax states of New York and New Jersey 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.

“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.”

A high-stakes meeting is set for Wednesday evening in Ryan’s office, where members from the most-affected states are expected to discuss options for addressing the deduction. 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.

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 Republican’s chief vote counter said things were on track for the budget’s passage Thursday but acknowledged that some members still needed convincing from Republican 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.”