ALBANY, New York — A largely blue-state tax issue will play an instrumental role in deciding the fate of House Republicans’ razor-thin majority this November. And they know it.

Republicans from swing House districts in high-tax areas of the country will spend the coming days lobbying their red-state colleagues to make changes to the $10,000 cap on state and local tax deductions that particularly hits suburban districts.

One of their arguments: Power in the House could be at stake.

“New York was the deciding factor between having a majority and not,” Hudson Valley GOP Rep. Mike Lawler, who campaigned heavily on the issue, said in an interview Thursday. “It will once again be deciding the majority.”

Lawler along with his fellow New York Republicans from battleground districts are backing a change to the provision known commonly as SALT. The cap on deductions would be raised to $20,000 for joint filers with gross adjusted income of $500,000 or less.

It passed the House Rules Committee on Thursday afternoon and could head to a floor vote as soon as next week.

“This is about fairness with our constituents being double taxed,” Lawler said. “This is pro-family. This is about ensuring married couples are not being penalized in the tax code.”

The SALT cap, part of the 2017 law approved under then-President Donald Trump and Republican-controlled Congress, hit costly Democratic-led states like New York, New Jersey and California the hardest.

Those states typically have some of the highest property taxes in the country. The first-term Republicans who flipped Democratic seats in suburban areas ran on the pledge of ending the cap.

But making changes has been a slog over the past 13 months for vulnerable House Republicans in a fractious GOP conference.

The plan to completely end the cap has been altered to a proposal that is tailored to mostly middle-income couples with the hope of creating a path of least resistance. Opponents have argued that lifting the cap would solely help rich people.

But in the New York area, a couple making $200,000 can easily have a property-tax bill that exceeds $20,000 a year. And not having the ability to deduct them from income tax filings can lead to higher household costs.

“Everyone knows they’re not going to lift the cap entirely, that’s just out of the realm of possibility,” a Republican aide said of the proposal and granted anonymity due to the sensitivity of the negotiations. “This is likely the most realistic and palatable thing for the conference.”

By narrowing it to married couples, supporters hope to expand the proposal’s appeal to more conservative GOP lawmakers.

“Regardless of whether the majority of those folks come from red states or blue states, we don’t punish people for being married,” Long Island freshman GOP Rep. Nick LaLota said.

The SALT cap has been decried by Democrats and Republicans alike in high-tax states, and it has for years served as red meat for candidates during campaigns in vital battleground races.

Former New York Gov. Andrew Cuomo blasted the SALT cap’s impact on New York homeowners and unsuccessfully sued to overturn it.

His successor, Democratic Gov. Kathy Hochul, this week said the issue is firmly in House Republicans’ hands, pointing to it as a reason why people are leaving for lower-taxed states.

“You can draw a line between the elimination of the full state and local tax deduction to the increase in outmigration from the state of New York,” she told reporters. “You can see that a lot of people left our state because that was just one more extraordinary burden that they used to be able to write off their property taxes.”

The fight over the cap on deductions has already spilled onto the campaign trail this year with six New York Houses likely up for grabs.

Democrat Tom Suozzi, a former House lawmaker who is campaigning for the seat he vacated in 2022 in a special election on Feb. 13, has long made repealing SALT a key plank. He told reporters Thursday that “it’s not going to get done” with Republicans in charge.

“These guys from Long Island who say they’re in favor of restoring the state and local tax deduction haven’t done anything to build a coalition,” he charged. “All they’re doing is bringing it up at the last minute.”

Mazi Pilip, Suozzi’s Republican-backed opponent, blamed her Democratic rival for not getting the SALT change while he was in office.

“Mazi is excited to see the fruition of the LI delegation’s hard work as they seek to raise the SALT cap that Tom Suozzi promised to restore, but failed repeatedly,” campaign spokesperson Brian Devine said.

House Minority Leader Hakeem Jeffries (D-N.Y.), a Suozzi ally, blamed Republicans for not including the SALT cap change in a broader tax package that cleared the chamber this week.

“My colleagues from New York came to the Congress last year and said their top priority was going to be to fix the state and local tax deduction that Republicans broke and they have failed to do it repeatedly,” he said. “I have no confidence in their ability to change that situation.”

The House tax bill, which included a strengthening of the child tax credit and relief for businesses, created a mini-revolt from some Republicans in Democratic-heavy states for not including the SALT change.

Freshman New Jersey incumbent Rep. Tom Kean, another vulnerable House member, was one of two New Jersey House members who voted against the tax relief bill Wednesday night.

“On a bill that does not raise the SALT cap deduction, I am a NO vote,” Kean said in a statement. “The fact is, families across New Jersey deserve SALT tax relief, and I will continue standing strong to deliver on that goal until we get a bill to the floor that extends that relief to New Jersey families.”

The other New Jersey member to vote against the tax bill was Democrat Frank Pallone. Democratic Reps. Bill Pascrell and Mikie Sherrill, two New Jersey members of the SALT caucus that is fighting for changes, have offered their own alternatives to lift the cap.

“Despite pervasive half-truths and misunderstandings, the state and local tax deduction is a lifeline for middle class Americans and their families,” Pascrell and Sherrill said in a joint statement.

LaLota, who voted against the tax bill, said it was a fulfillment of his campaign pledge to change the SALT cap. GOP Rep. Marc Molinaro, who voted in favor of the tax bill, said in an interview that the tax bill approved this week is meant to build a “foundation” moving forward for broader relief.

House Democrats, he insisted, should also go along with the SALT change.

The outcome of next week’s vote could be used by both parties on the campaign trail: Failure would be trumpeted by Democrats; success praised by Republicans.

“This is an opportunity for Democrats to show they’re bipartisan,” Molinaro said in an interview. “Either they agree with what they’ve been saying or they see this as a political tool for them.”

Jason Beeferman, Nicholas Wu and Dustin Racioppi contributed to this report.