It could in theory be a perfect solution for President Trump — a “border adjustment tax” that helps him deliver corporate tax relief or a big infrastructure package, while potentially bolstering U.S. manufacturers and allowing him to claim that his marquee campaign promise to build a wall on the U.S.-Mexico border has been paid for.

But it might never happen.

Trump first panned the idea as “too complicated.” Then his press secretary floated it late last month as a way to make Mexico pay for the wall. Soon after, the White House started to back away, claiming that the policy shift being pushed by House Speaker Paul D. Ryan (R-Wis.) is only one of many options under discussion.

The early tensions over the tax plan and the mixed signals being sent by the White House provide a glimpse into what could become a major intraparty rift as Congress considers how to pay for the border wall and enact new tax cuts.

House Republicans are counting on a windfall from a border adjustment tax to fund broader tax relief, but Senate Republicans remain cool to the idea, with some even mocking its potential consequences.

“Simply put, any policy proposal which drives up costs of Corona, tequila, or margaritas is a big-time bad idea,” Sen. Lindsey O. Graham (R-S.C.) said in a tweet. “Mucho Sad.”

The White House’s position is, at best, inconsistent.

“This is a source of very heated debate, even within the conservative community,” said Stephen Moore of the Heritage Foundation, a proponent of the border adjustment tax who advised Trump during his campaign. “It’s not going anywhere if you can’t at least rally Republicans around it.”

Moore lamented that he did not spend more time pushing the idea on Trump when he had his ear. “I never had a chance to sit down and explain it to him. If I had, I think I could have told him it would accomplish a lot of what you want to do.”

Democrats are poised for the fight, promising to argue that the tax would raise the cost of imported merchandise at Walmart and other retailers, hitting the very working-class voters who helped carry Trump to victory.

Republicans also are facing a political dilemma of their own making. After years of deriding any tax increase as a burden on the economy, they find themselves trying to sell a more nuanced view, arguing that the border adjustment tax will be good for the taxpayers overall, even if it hits some businesses and consumers more than others.

Under the House Republican plan, corporations would no longer have to include sales from exports when calculating their income for tax purposes. Meanwhile, profits on exports would be free of taxation.

In the short term, the plan would generate a lot of money for the federal government. Since the United States imports more than it exports, the new taxes on imports would more than make up for the big break on exports. The plan would yield about $1.2 trillion over 10 years, according to the nonpartisan Tax Policy Center.

That could allow Trump to move forward with a plan to cut corporate taxes to 15 percent from the current level of 35 percent.

The proposal could bolster the manufacturing sector, including in Rust Belt states such as Michigan, Wisconsin, Pennsylvania and Ohio that propelled Trump to the White House. Boosters of the House GOP plan say that the new system would be a boon for U.S. producers who compete with goods and services from overseas — although there is disagreement among economists about whether the system would accomplish that goal.

And, as the White House suggested, a small fraction of the revenue raised from the tax could fund the $12 billion to $15 billion estimated cost of Trump’s wall — though whether that meets the definition of Mexico “paying for” the wall is another matter.

Longtime Washington observers say it’s possible that the fate of the House GOP tax plan could become intertwined with that of Trump’s promise for a massive infrastructure package — an idea about which Republican leaders are lukewarm. Both initiatives are likely to be taken up in earnest in the spring.

Trump has said he would like to see more than $1 trillion invested in the nation’s aging roads, bridges, airports and other critical infrastructure, though that initiative is expected to rely heavily on private-sector spending.

If Trump comes on board, he faces a major sales job in the Republican-controlled Senate, said Jim Manley, a former senior aide to former Senate minority leader Harry M. Reid (D-Nev.).

“The question is whether he could move them by the sheer force of his personality or an onslaught of tweets,” said Manley, now a Washington lobbyist.

The border adjustment tax being pushed by House Republicans differs from the “border tax” that Trump mused about on the stump and on Twitter. Trump has been vague about his intentions, but the tax could be focused more punitively on particular companies and raise only a fraction of the revenue envisioned under the House GOP plan.

Proponents of the broader House plan say that the current international tax system unfairly penalizes American companies.

“We lose both here and abroad,” Rep. Kevin Brady (R-Tex.), chairman of the House Ways and Means Committee, recently told the U.S. Chamber of Commerce. “This means today Chinese steel is cheaper here in the U.S. than American steel. Mexican beef and autos are cheaper than American beef and autos. Foreign oil is cheaper than American oil.”

Many economists, however, doubt that the GOP plan would have any real benefits for U.S. firms competing with foreign companies. They argue the price of the dollar in global currency markets would climb in response to the tax, canceling out any advantages for U.S. producers. A strong dollar makes U.S. exports relatively more expensive, and imports relatively cheaper.

Trump’s only public comments about the border adjustment tax have cast cold water on the idea. In a recent interview with the Wall Street Journal, he called the idea “too complicated.”

But that was before the kerfuffle late last month, when White House press secretary Sean Spicer told reporters that a 20 percent tax on goods coming in from Mexico would cover the cost of building the border wall.

His comment was widely interpreted as an endorsement of the broader House GOP plan — but Spicer and other White House aides said later in the day that it was meant as just one possible way for paying for the wall.

Adding to the confusion, Peter Navarro, the head of Trump’s National Trade Council, went on CNBC the following day and said, “There’s no question that we need a border adjustable tax of some kind.” But, he added, “It’s one that has to be flexible.”

Navarro suggested that Japan and Germany be treated differently, for example, which is not what the House GOP plan envisions.

Navarro was also asked what other leading advisers to Trump think about the idea.

“They should speak in their own words,” he said, adding that he was sharing only his views.

A request by The Washington Post to interview Navarro was referred by the White House to Gary Cohn, director of the National Economic Council. Cohn’s office said he was unavailable. In a CNBC interview Friday, Cohn said a border adjustment tax is “one of the options that is on the table” and suggested that revenue from the tax could help the administration achieve its other goals.

Trump advisers began tax talks in early January in a meeting with Ryan and his team. Even aides to Ryan acknowledge there is a major education effort ahead to get lawmakers and others to understand the border adjustment tax proposal.

But the lack of consensus among economists over the benefits and drawbacks of the idea has made rallying support behind it challenging.

The Republican plan “has turned out to be like a Rorschach test,” said Edward Kleinbard, a legal scholar at the University of Southern California. “People can see in it anything they choose.”