When President Trump signed his new Nafta accord last month with the leaders of Mexico and Canada, Prime Minister Justin Trudeau almost didn’t show up. The reason: Mr. Trump still hasn’t lifted the steel and aluminum tariffs as he promised he’d do if America’s two neighbors signed a revised trade deal.

A month later they’re still waiting. The delay is damaging the U.S. economy and America’s credibility as a trading partner. Though Mr. Trump likes to use tariff threats as a negotiating tactic, his Administration also promised relief from the levies he imposed under Section 232 of U.S. trade law.

Commerce Secretary Wilbur Ross told Congress in June that the “objective” of the metals tariffs “is to have a revitalized Nafta, a Nafta that helps America and, as part of that, the 232s would logically go away, both as it relates to Canada and as to Mexico.”

In July U.S. Trade Representative Robert Lighthizer told a Senate hearing that “resolving the NAFTA issue—we would expect, or hope, that we would resolve the steel and the aluminum issues with both Mexico and Canada.”

Last March no less than the President himself tweeted that “tariffs on Steel and Aluminum will only come off if new & fair NAFTA agreement is signed.”

Yet U.S. officials now say signing new Nafta isn’t enough. They also want Canada and Mexico to agree to new quotas on their metals exports to the U.S. before the U.S. will lift the Section 232 tariffs. This is politically managed trade that responds to lobbying in Washington, not free trade that responds to market supply and demand.

Canada is the largest foreign supplier of steel to the U.S., with a 20% import share, so the goal of quotas would be to limit steel supply to keep prices in the U.S. high. Canada and Mexico are understandably resisting since they thought a new Nafta would mean the end of arbitrary tariffs imposed in Washington.

Meanwhile, American steel consumers continue to suffer from the tariffs. One loser is the American beer industry, which says the tariffs amount to a $347 million tax on U.S. brewers. Beer Institute President Jim McGreevy says U.S. brewers used more than 36 billion aluminum bottles and cans last year and the tariffs “could cost the beer industry more than 20,000 jobs.”

Hundreds of American metal fabricators are also finding it difficult to acquire the steel to compete with foreign producers. Riverdale Mills Corp., in Northbridge, Mass., makes “aquamesh,” a marine wire-mesh used in 85% of lobster traps made in North America. The company is the largest global supplier for lobster fishermen and makes 95% of the wire mesh used for oyster cultivation. It exports 45% of what it makes.

Riverdale needs specialty steel, which CEO James Knott says the company would like to buy in the U.S. But suppliers often can’t make the high-quality grade he needs and his steel prices have doubled since January. He’s losing market share at home and abroad.

“My foreign competitors are buying steel at half the price I’m paying, and some of them face no tariffs when [exporting] to the U.S,” he says. The company has received some exclusions, but they account for less than 3% of their steel purchases. Mr. Knott says he’s cut his workforce to 150 from 200.

New Nafta opens a slightly larger share of the Canadian dairy market to U.S. producers. But Mexico is the largest destination for U.S. dairy exports, and American dairy farmers are getting hammered by the 25% tariff that Mexico imposed on U.S. dairy products in retaliation for the steel and aluminum tariffs. The marginal gain in Canada may not make up for the export losses to Mexico.

“We’re not ready to celebrate,” CEO David Ahlem of Hilmar Cheese Co., based in Hilmar, Calif., said when new Nafta was announced in October. “As long as 232 retaliatory tariffs are still in place . . . we can’t enjoy the benefits of having a modernized NAFTA and be back to where we were.”

Mr. Trump’s broken Nafta promise will make it harder to negotiate new trade deals with Europe and Asia. Other countries worry that even if they sign a new deal, Mr. Trump or some future U.S. President will roll out 232 tariffs any time there’s domestic political pressure. Congress intended 232 to be used for “national security” emergencies, not as an all-purpose trade weapon. Mr. Trump’s tariff trickery with Mexico and Canada is one more reason Congress should restrict his 232 license.