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House GOP leaders committed to putting a targeted tax bill up for a House floor vote next week to appease blue-state Republicans who were angry over its exclusion from a bipartisan tax deal expected to pass Wednesday, sources told Fox News Digital.

A group of New York Republicans almost tanked a normally sleepy procedural vote known as a "rule" vote on Tuesday in a protest of the bipartisan legislation announced earlier this week.

They were frustrated it did not address the state and local tax (SALT) deduction cap, an issue that's critical to Republicans in the politically fickle suburbs outside of major cities like New York City and Los Angeles. They also were furious at being sidelined by GOP leaders' decision to have the tax deal bypass its own procedural hurdle and get a vote under suspension of the rules, likely out of concern for similar protests.

But Speaker Mike Johnson, R-La., narrowly avoided disaster on Tuesday afternoon when the four Republican rebels switched their votes from "no" to "yes," passing the rule along party lines. It's a rare mutiny from Johnson's moderate flank, in contrast with the ultra-conservative House Freedom Caucus, which has weaponized several rule votes this term.

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Speaker of the House Mike Johnson

Speaker Mike Johnson committed to addressing the SALT issue during a meeting last night, two sources said. (Kent Nishimura/Getty Images)

Rep. Nick LaLota, R-N.Y., one of the Republicans who protested, told reporters afterward that Johnson committed to meeting with members of the "SALT caucus" to find a possible way forward.

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What resulted from those hours of meetings was a promise by Johnson and Ways & Means Committee Chairman Jason Smith, R-Mo., to bring a separate SALT deduction cap bill to the floor aimed at removing the statute's "marriage penalty," according to two sources familiar with the discussions.

It would raise the maximum cap to $20,000 for married couples filing jointly, versus the current $10,000 limit that applies to both single and joint returns, according to one of the sources. The proposal would also be aimed at providing more targeted relief for middle class families, the source said.

A House GOP leadership source stressed that the timeline of a possible chamber-wide vote is fluid and noted the bill would need buy-in from the Rules Committee and GOP Conference. 

New York Republicans

Long Island Republican Congressmen Nick LaLota, left, and Anthony D'Esposito were among those fighting for a SALT deduction cap increase. (Getty Images)

The details of what would be in an eventual SALT deduction cap proposal also haven’t been worked out, that source said, adding that multiple possibilities were raised at the Tuesday night meeting.

A spokesperson for the speaker's office told Fox News Digital, "Speaker Johnson and Chairman Smith agreed that they would continue working with members to find a path forward for legislation related to SALT."

There was no cap on state and local levies people could deduct from their federal taxes before 2017, when the Tax Cuts and Jobs Act was passed.

The SALT deduction cap is a politically contentious issue and is unique in that it does not fall evenly across party lines. 

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Republicans in places like New York and California have argued that it provides necessary relief for middle-class families living in expensive areas. 

Lawmakers in more rural areas claim it further lines the pockets of high-income earners – a concern the new targeted proposal is seeking to alleviate.

Mike Garcia

Rep. Mike Garcia previously argued that SALT deduction caps would be an election issue. (Getty Images)

Meanwhile, Republicans from districts affected by the SALT cap have warned that Congress' action on the issue – or lack thereof – could decide who holds the House of Representatives next year.

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"We can address this right now, on our terms, get a win out of it politically," Rep. Mike Garcia, R-Calif., told Fox News Digital last week. "Or we can do nothing, lose potentially a lot of races because we passed this opportunity to address SALT, which is very important to New York and California, and then try to have a conversation about the new policies when… we've lost the majority because we passed this opportunity to help the swing district members get a win on the SALT cap."