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.

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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.

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.

Further details were not immediately available.

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.

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

"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." 

Fox News Digital reached out to the Ways & Means Committee and the speaker's office for comment.