House GOP leaders’ push for a tax on imported goods hit the skids in Congress, and they are looking for support from President Trump to keep the plan alive, but the White House only toys with the idea.

The 20 percent across-the-board tax on imports, known as the border adjustment tax, is the linchpin of House Republicans’ tax reform blueprint. The new revenue stream would lay the foundation for a new tax structure and pay for a proposed massive cut to the corporate tax rate.

The tax likely will top the agenda when Mr. Trump meets Thursday with executives from top U.S. manufacturing firms.

Opponents of the border adjustment tax, including major U.S. retailers and anti-tax conservatives, warned that it would be passed on to consumers, driving up prices of everything from underwear to cellphones. Pretty soon, rank-and-file House Republicans split on the proposal and Senate Republicans overwhelmingly bucked the idea.

Sen. Lindsey Graham warned that a border adjustment tax “won’t get 10 votes in the Senate.”

The resistance threatens the entire tax reform package spearheaded by House Speaker Paul D. Ryan and House Ways and Means Committee Chairman Kevin Brady.

So far, Mr. Ryan and Mr. Brady can’t count on help from the Republican in the White House.

But neither can the opponents.

“We’re all just waiting to see,” said Doug Sachtleben, spokesman for the conservative low-tax advocates Club for Growth that is pressuring lawmakers against the tax.

Mr. Trump’s initial reaction was to recoil form the border adjustment tax, saying it was “too complicated.”

He told The Wall Street Journal last month that “usually it means we’re going to get adjusted into a bad deal.”

Two weeks later, however, Mr. Trump seemed to endorse the idea as a way to make Mexico pay for a wall on the U.S. border.

“We’re working on a tax reform bill that will reduce our trade deficits, increase American exports and will generate revenue from Mexico that will pay for the wall if we decide to go that route,” he said in a speech to House and Senate Republican on a retreat in Philadelphia to hammer out their legislative agenda.

White House press secretary Sean Spicer that day told reporters the border adjustment tax would “easily pay for the wall.”

“By doing it that way, we can do $10 billion a year and easily pay for the wall just through that mechanism alone,” he said.

Within hours Mr. Spicer backed off the plan, saying the border adjustment tax was one of many options under consideration, and he was just making a point that “generating revenue for the wall is not as difficult as some might have suggested.”

Earlier this week Mr. Spicer remained noncommittal when pressed by a reporter at the daily White House briefing about the border adjustment tax.

“The president’s been very clear that in the next couple of weeks, we expect to have a tax plan that gets out there,” said Mr. Spicer. “That is being worked on continuously. And so I’m not going to get in front of that.”

Mr. Brady, the Texas Republican at the helm of the Ways and Means Committee, insisted that he’s not worried about the opponents in his party, and will not give up on the border adjustment tax.

“At the end of the day, it is going to be part of the tax reform blueprint,” he said in an interview on Fox News Business’s “Varney & Co.” program.

He said the current tax system puts U.S. companies at a disadvantage because almost every other country slaps a tax on imports.

“It’s pro-growth and pro-consumer. We eliminate every tax incentive to move jobs overseas,” he said. “We are building support every day for taxing products equally in the United States, and people are slowly starting to realize that it is key to lower tax rates for businesses of all sizes.”

The border adjustment tax got a boost from 16 CEOs from some of America’s largest companies who vouched for the tax plan in a letter to Congress leaders. The CEOs from companies including Boeing, Caterpillar, Dow Chemical, Eli Lilly, GE, Oracle and Pfizer called it a “more competitive ‘territorial’ approach to taxing business.”

Tony Simmons, CEO of Tabasco maker McIlhenny Company, said he supported the border adjustment tax from the perspective of a business that both imports and exports.

“The border adjustment works both ways for us. We feel as though it’s a potential benefit primarily because of the tax implications it has moving forward,” he said.

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