The House is preparing legislation to cut federal taxes for relatively high-income married couples in high-tax states, a measure meant to placate politically vulnerable Republicans who last week nearly held up another tax relief measure for working families to force a vote on the issue.

The legislation, sponsored by Rep. Michael Lawler (R-N.Y.), would raise the cap for the state and local tax deduction, known as SALT, for married couples who file taxes jointly and make up to $500,000.

Congress had capped the deduction both for individuals and couples at $10,000 to help pay for President Donald Trump’s 2017 tax cuts. Lawler’s bill, which has support from a phalanx of other Republicans from Democratic-controlled states, would let married couples offset up to $20,000 of income on their federal returns with state and local taxes for the current tax year. The cap would drop back to $10,000 in 2024 until it expires in 2026.

The bill, though, is entangled in larger disputes over which factions of the raucous GOP conference control the House, how Republicans will attempt to hang on to the chamber in November’s elections and the early skirmishes in the debates that will ensue when the Trump tax cuts expire in 2025.

The House last week passed another tax bill to expand the child tax credit, mostly claimed by working parents, and restore certain corporate tax breaks. The measure, which still must pass the Senate, could lift 400,000 children out of poverty, according to nonpartisan estimates.

The balance in that bill satisfied members of both parties — mostly Democrats for the tax credit expansion and mostly Republicans for the business provisions, though each part of the deal had support in both parties — and helped lawmakers build up their tax policy priorities ahead of a larger legislative push expected at the end of the year.

But residents of high-tax states who used to be able to deduct their entire state and local tax bills — property and income taxes alike — have been pushing to change the SALT cap since the 2017 tax bill.

Even at the $10,000 cap, the deduction is still mostly taken by wealthier tax filers, who earn enough to owe larger state and local tax bills and have enough other deductions to make it worth itemizing rather than taking the standard deduction, which is worth $27,700 for married couples filing jointly this tax season.

The nonpartisan Tax Foundation found that the vast majority of the benefits of doubling the cap would go to couples who earn more than $200,000, and between a third and half of them would see a tax cut. A different nonpartisan estimate by the Penn Wharton Budget Model at the University of Pennsylvania found that the legislation would cost $12 billion in lost federal tax revenue.

But Lawler and other New York and California Republicans represent districts that President Biden carried in 2020, and they may face longer odds to reelection after liberal state legislatures redraw congressional districting maps. Bringing home a SALT expansion, the lawmakers say, could be key to the economic planks of their campaigns.

“I haven’t seen the politics or polling on this specific issue or a specific race, but I’m quite familiar that all Long Islanders, and the ones in the third district in New York, want this town to come together and give them a little more SALT,� said Rep. Nick LaLota, one of the New York Republicans.

In high-tax states, the deduction was quite valuable before it was limited: The Tax Foundation found that in the last year, without the cap, the deduction accounted for as much as 2.5 percent of adjusted gross income in Maryland, 1.8 percent in California and 1.53 percent in New York.

Conservatives from elsewhere in the country have called lifting the SALT cap a “blue state� tax cut. Republican strongholds like Texas, Florida and Tennessee have no state income tax, rendering the SALT deduction less relevant for residents in those states.

That dynamic has forged unorthodox alliances in Congress: Liberals from states that could benefit from a more generous SALT cap have teamed with traditional anti-tax conservatives; Republicans from low-tax states have joined with progressives who oppose what they see as a tax cut for the wealthy at the expense of low-income earners.

Rep. Bill Pascrell Jr. (D-N.J.) attempted to amend the child tax credit bill to substantially raise the SALT deduction for both single and joint filers. It failed to gain any Republican support.

“For years, Democrats have worked to undo the damage done by the Trump tax law, which established a SALT cap that increased taxes for families, including thousands of Marylanders,� said Rep. David Trone (D-Md.), who is also running for Senate there.

Rep. Chip Roy (R-Tex.), a spending hawk and member of the archconservative House Freedom Caucus, was the lone GOP member of the House Rules Committee, which determines which bills advance to the floor, to vote against the SALT legislation.

Rep. Tom Cole (R-Okla.), the committee’s chair, voted to let the bill advance but later signaled that he leaned toward opposing it.

“Everybody should pay the same federal taxes,� he told The Washington Post. “I don’t like situations where we enable people to have higher state and local taxes at the expense of federal revenues.�

The tax bills have drawn House Speaker Mike Johnson (R-La.) into a new rift inside his conference. Republican infighting has led the speaker to leverage Democratic votes to clear procedural hurdles erected by the Freedom Caucus, whose members are furious about Johnson’s approach to spending issues. He’s often leaned on the New York Republicans — Lawler, LaLota, and Reps. Andrew R. Garbarino and Anthony D’Esposito — who are viewed as more moderate, for crucial votes to move legislation.

But when the House moved to pass the child tax credit expansion and corporate tax cuts, the legislation’s authors, Rep. Jason T. Smith (R-Mo.) and Sen. Ron Wyden (D-Ore.), chairs of Congress’s tax-writing committees, did not include the New Yorkers’ preferred SALT provision.

“Tax bills are about choices, and tough ones,� Wyden told The Post. “I try to recognize that tax bills are really about fairness and giving everybody a chance to get ahead. That’s how we can encourage our businesses, particularly a small businesses.�

The New York House members took a page from the Freedom Caucus and threatened to throw up their own procedural hurdles for the child tax credit bill last week, only backing down when Johnson agreed to advance a separate bill for SALT.

If it were to pass the House, though, the bill faces long odds in the Senate, though opinions there on the SALT provision are mixed. Democrats considered lifting the cap during negotiations on Biden’s Build Back Better agenda, but those proposals ultimately stalled due to opposition from progressives and conservatives alike.

“All the SALT deduction did, capping it, is make sure that blue states don’t get subsidized by red-state taxpayers,� Sen. John Cornyn (R-Tex.) said last week. “I think providing a cap at $10,000 was a way to make it fair. But I know the blue states would love to have the red states subsidize their high spending in the big cities.�