Congressional Republicans reached a deal Wednesday on a sweeping overhaul of the nation’s tax laws, paving the way for final votes next week on a bill that slashes taxes for businesses and the wealthy and offers more modest breaks for many others.

The agreement would set the top individual rate at 37 percent, down from today’s 39.6 percent, giving the wealthiest Americans a major break.

The corporate rate would be 21 percent — down from 35 percent but higher than the 20 percent President Trump called for.

The changes would take effect in 2018.

House and Senate negotiators also agreed to partially retain the so-called SALT deductions for state and local income and sales taxes, as well as property taxes, but to cap them at a combined $10,000.

That change helps renters in high-income, high-tax states like New York, New Jersey and Connecticut, who don’t pay property taxes.

But some GOP lawmakers from New York complained it wasn’t enough. Reps. Dan Donovan (R-SI), Peter King (R-LI) and Lee Zeldin (R-LI) asked Trump to intervene directly to ensure the tax bill doesn’t hurt their middle-income constituents.

“We’ve run the numbers, Mr. President,” they said in a letter to the president.

“Under the tax bills currently under consideration, many middle-income New Yorkers living in modest homes would pay more in taxes. They just cannot afford it.”

Negotiators also agreed to let homeowners deduct interest on the first $750,000 of a new mortgage, down from the current limit of $1 million.

And the deal was expected to eliminate the alternative minimum tax for corporations — though GOP lawmakers did not release all of the details.

Sen. Susan Collins (R-Maine) said she opposed lowering the top rate but would not say whether that was a deal-breaker.

“I don’t think lowering the top rate is a good idea. I’m going to wait and look at the entire conference report and see what all the provisions are,” she said.

The measure, if passed, would give Trump his first major victory in Congress.

The plan has come under assault by Democrats, who say it is unfairly tilted in favor of businesses and the wealthy.

Top Senate Democrat Charles Schumer said Wednesday GOP leaders should delay a final vote until Sen.-elect Doug Jones (D-Ala.) is sworn in.

“It would be wrong for Senate Republicans to jam through this tax bill without giving the newly elected senator from Alabama the opportunity to cast his vote,” Schumer said.

“That’s exactly what Republicans argued when [former Massachusetts GOP Sen.] Scott Brown was elected in 2010.”

But the GOP leadership planned to push ahead.

Trump touted the plan during an event at the White House that featured several middle-class families praising the plan and thanking the president.

“Our current tax code is burdensome, complex and profoundly unfair,” Trump said. “It has exported our jobs, closed our factories and left millions of parents worried that their children might be the first generation to have less opportunity than the last. I am here today to tell you that we will never let that happen.

“We’re reclaiming our destiny as Americans. When the government loosens its grip, there is no summit we can’t reach.”

The president predicted the tax bill would pass Congress without any votes from Democrats “for political reasons” — even though many of them like it.

If Congress sends him a bill before Christmas, he said, the IRS has confirmed there would be lower taxes and bigger paychecks starting in February.

Trump called it “a giant tax cut for Christmas” and predicted that the average middle-class family would save about $2,000.

But the plan remains highly unpopular, according to a new Quinnipiac University poll.

Voters disapprove of it by 55 percent to 26 percent, the survey found. Just 16 percent said the plan would reduce their taxes, while 44 percent said it would increase them. Thirty percent said it would have no impact.

Additional reporting by Marisa Schultz with Post wires