Besides those objections, there could be a more basic problem with the plan: The tax on imports — part of what is known as “border adjustment” — might not provide the revenue its supporters are banking on.

That's according to an article published Monday in Tax Notes that, should its predictions be borne out, would undermine a primary rationale for the proposal and make it far harder for Republicans to deliver on other tax cuts while still balancing the budget.

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The article is by a pair of former senior economic officials who served in the Obama administration, David Kamin and Brad Setser, but they use an argument that conservative lawmakers might find congenial. A border adjustment produces revenue for the federal government only as long as Americans are, on net, borrowing money from foreigners on net — and Kamin and Setser argue that the current pace of borrowing cannot continue forever.

On net, Americans buy imports from abroad by borrowing money from foreigners. If Americans borrow less, they can buy less, and if imports decline, the border adjustment would generate less money for the government.

Indeed, President Trump has promised that his skills as a negotiator will lead to better trade deals, driving down net imports by giving domestic companies the upper hand.

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But if Trump delivers, that could be a problem for Republicans, who hope to avoid a Democratic filibuster in the Senate when they move a tax-reform bill through Congress. To ensure that their legislation is immune to a filibuster, Republicans need to make sure that their proposal would not force the federal government deeper into debt in the long term.

If Congress's independent budgetary referees predict that Republicans' new system might not stay in the black, Democrats could stymie the plan.

A border adjustment would address that problem by raising money through what is effectively a new tax on imports — barring companies from deducting the cost of any imported goods or services from their income, as they do now — but the border adjustment is not just a tariff.

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It is also a subsidy for exports. Corporations would not have to pay taxes on their income from sales overseas.

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The logic of combining the two is that doing so would simplify corporate taxes, allowing businesses to ignore any transactions involving foreign customers or suppliers. The combination would also prevent companies from shifting their U.S. profits abroad, out of the reach of federal authorities, by exaggerating the cost of their imports or lowballing the value of their exports.

Proponents have other reasons for supporting a border adjustment. Economists say the plan probably would result in more hiring. Companies could shift production to the United States and export their goods back out of the country to their customers around the world, effectively without paying taxes.

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Republicans included a border adjustment in a tax-reform proposal last year.

“Today our broken tax code favors foreign goods over American goods and encourages businesses to shift jobs and profits out of the United States and into foreign countries solely for tax reasons,” Rep. Kevin Brady (R-Tex.) said in a statement. “Our ‘built for growth’ tax reform blueprint will reverse that trend.”

Brady, the chairman of the Ways and Means Committee, reiterated that the final version of the Republican plan will not require the government to borrow more. Republicans are seeking “fiscally responsible, deficit-neutral reform,” he said.

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To generate revenue, the border adjustment plan relies on U.S. businesses and consumers importing more than they export — that is, the United States must have a trade deficit. Otherwise, the export subsidy will become too costly.

The country has had a trade deficit for decades, but Kamin and Setser argue that imports are likely to decline relative to exports eventually. Every year that imports exceed exports, the U.S. economy must essentially borrow money from abroad, a process that the pair write will not continue at the same pace indefinitely.

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After all, foreigners do not send their products to the United States for free. They receive a variety of IOUs in return, financial obligations such as corporate debt and Treasury bonds. Eventually, Americans will have to make good on those obligations.

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Kamin and Setser assume that Americans' debts to foreigners will eventually stop increasing, relative to the overall economy. Foreign investors will become skeptical of the ability of U.S. borrowers to repay their debts, so it would be more difficult for American businesses and consumers to obtain the credit they need to buy products from abroad. Reduced demand for American financial obligations would reduce the demand for the dollar in currency markets, making U.S. exports cheaper and more attractive.

In their article, Kamin and Setser estimate that the trade deficit will eventually stabilize at between 0.5 percent and 1.5 percent of the gross domestic product in any given year. That is a broad range, and the pair do not offer estimates of how rapidly the trade deficit will decline.

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Forecasting the trade deficit involves a fair amount of guesswork, said Alan Cole, an economist at the Tax Foundation, which supports reducing rates. “You could see a trade deficit run for a long time, and that’s what we’ve seen in the U.S. for 30 years now,” he said.

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Yet he described Kamin and Setser's argument as a plausible one, and their figures are well below the current level of about 2.5 percent, used in an analysis last year by the nonpartisan Tax Policy Center. With fewer imports and more exports, the border adjustment will generate less revenue for the government.

In any case, the important question is not exactly what the trade deficit would be in any particular year, but how congressional referees at the nonpartisan Joint Committee on Taxation will approach the difficult problem of predicting it. If the committee produces a range of estimates suggesting that it is possible that the border adjustment would not pay for Republicans' proposed tax cut, the plan would be exposed to a Democratic filibuster.

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“It’s definitely possible that a border adjustment tax helps a plan achieve revenue neutrality over 10 years, but leaves in place a shortfall,” said Ed Lorenzen of the Committee for a Responsible Federal Budget, which advocates reducing federal borrowing.

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Republicans would have a few options to avoid that ruling. They could offer less tax relief over the long term in their proposal, or they could combine tax legislation with reductions in spending elsewhere in the budget, such as in Medicaid, the federal program that provides health insurance to the poor.

If projections for revenue from the border adjustment over the decades to come do little to help Republicans avoid a filibuster, then the political case for including the controversial proposal could be weakened.

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Alternatively, Republicans could avoid Democrats in the Senate altogether by putting forward a plan that would expire after 10 years, the approach they adopted when they reduced taxes under President George W. Bush. They could also rely on a different set of estimates than those produced by the Joint Committee on Taxation if that agency's analysis is unfavorable to their plan.

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For instance, GOP lawmakers could ask the Trump administration to forecast the trade deficit instead. Whether the administration will support their plan remains to be seen, however.

On Thursday, Commerce Secretary Wilbur Ross told CNBC that the Trump administration has not yet taken a position on the idea, known as a border adjustment, but is studying it carefully.