The scene looked hopeful at first glance. A social media post by President Karin Keller-Sutter of Switzerland showed her smiling and shaking hands with U.S. Secretary of State Marco Rubio in Washington on Wednesday, at a hastily arranged meeting after President Trump had blindsided Switzerland with a punishingly high tariff.

“We discussed bilateral cooperation, the tariff situation, and international issues,” Ms. Keller-Sutter said of the meeting with Mr. Rubio. But what she didn’t have was a trade deal. So, on Thursday Switzerland found itself in the uncomfortable position of facing a 39 percent tariff on its goods in the United States, one of the highest rates in the world.

Swiss officials are trying to untangle how their country went from being a longtime ally of the United States to an apparent pariah in the eyes of Mr. Trump. After returning to Switzerland early on Thursday, Ms. Keller-Sutter went straight to an emergency meeting of her government to figure out what course to set for further negotiations.

At a news conference after the meeting, she said that officials would “continue discussions with Washington,” and had already “optimized” Switzerland’s offer, without giving details. They wanted a deal with the United States that would lower tariffs, “but not at any price,” she said.

For Mr. Trump, the biggest issue is reducing the $40 billion U.S. trade deficit with Switzerland, and the Swiss had not done enough to address that, said a U.S. official familiar with the talks, speaking on condition of anonymity to describe sensitive discussions.

Guy Parmelin, the Swiss economy minister, said at the conference that the country’s industries would be hit hard by the high tariff rate as well as the uncertainty over when and whether it might be reduced. To shield the economy from the prospect of “mass layoffs,” the government would extend a furlough program that companies can use to keep employees on standby, he said.

Swiss business groups have warned of a catastrophe for industries that export to the United States, including makers of watches, industrial machinery, chocolate and cheese.

“The worst-case scenario has become a reality,” Swissmem, which represents the Swiss engineering and tech industries, said in a statement. “If this exorbitant customs burden is maintained, the Swiss tech industry’s export business to the U.S.A. will be effectively annihilated.”

The crisis has reignited a longstanding debate in Switzerland over whether to remain independent from the European Union, which faces a 15 percent tariff as part of a deal with Mr. Trump, or whether the country should join the bloc as a way of shielding itself from the storms blowing from Washington.

Members of Switzerland’s Social Democratic Party have been calling on the government to push for greater integration with Europe. Switzerland already took a step in that direction in June, when the government approved a package agreed upon with the European Union to streamline their trade ties after a decade of thorny negotiations.

In the meantime, Mr. Trump’s tariff shock has prompted Swiss executives to turn to a series of contingency plans, few of them desirable.

Georges Kern, the chief executive of the luxury Swiss watch brand Breitling, said in an interview that the company had enough inventory in the United States to last roughly three months. “We need to evaluate price increases, not only in the U.S.A. but also around the globe, to balance the costs due to the tariffs,” he said, noting that the company would discuss sharing the burden with retail partners, including accepting lower profit margins.

If the U.S. tariff on Swiss goods remains at 39 percent for a prolonged period, however, the watchmaker would consider cutting costs and reducing investments in the United States. Mr. Kern hoped for a trade agreement in the coming weeks, and said that Swiss companies “can and will contribute to find a solution with President Trump to address his concerns.”

Pierre-Yves Bonvin, the chief executive Steiger Textil, a Swiss company that makes industrial knitting machines, described the tariffs as a “tsunami.” Swiss businesses had been led by the government to believe that they would face a top tariff of 15 percent, he said, which they could have managed. A 39 percent tariff led him to question whether it was worth selling in the United States anymore, he added.

Another problem is that 70 percent of Steiger’s exports go to German companies, many of which had planned to set up shop in the United States to avoid Mr. Trump’s tariffs. Those clients would potentially still have to pay a steep tariff on his machines if they brought them to the United States, given a new tariff on so-called transshipments.

A Swiss maker of precision cutting tools said that his company would start layoffs almost immediately for its small American work force of 10 people because it could not afford to absorb the 39 percent tariff, nor pass the whole price increase onto its American manufacturing customers. The dimming prospects for business in the United States also drove the decision, according to the company’s chief executive, who spoke on condition of anonymity because he feared retaliation by Mr. Trump or U.S. customs authorities against him or his company.

The Swiss government’s focus now is getting talks back on track. Officials thought they had made a convincing case to their American counterparts to reduce an initial 31 percent tariff threat by highlighting the major investments that Swiss companies have made in the United States, including by the pharmaceutical giants Roche and Novartis.

That paved the way for what the Swiss thought would be a perfunctory phone call between Ms. Keller-Sutter and Mr. Trump, but their conversation went off the rails.

In a CNBC interview on Tuesday, Mr. Trump expressed irritation with the call. “The woman was nice but she didn’t want to listen,” Mr. Trump said of Ms. Keller-Sutter, stressing that the tariff rate was related to the large trade deficit the United States has with Switzerland.

Mr. Trump’s recent focus has been on wrangling big deals with big economies, announcing agreements with the European Union and Japan that reduced tariffs in exchange for huge investments in the United States and energy purchases from American producers.

Switzerland has a population of just nine million. But officials argued that their companies invest more in the United States than any other country per capita. The country had eliminated import taxes recently on all goods except agriculture, so nearly all American goods face no tariffs. They tried to explain that three-quarters of the trade deficit with the United States was because of gold bullion and bars refined in Swiss foundries, which do not face tariffs.

As Switzerland discusses what officials have called a “more attractive offer,” it has some options, analysts said. Mr. Trump has expressed interest in countries lowering non-tariff barriers, such as value-added taxes. He is also irked by high tariffs on U.S. agricultural goods.

The United States labeled Switzerland a currency manipulator during Mr. Trump’s first term, after the Swiss central bank intervened in the foreign exchange market to manage the rise of the Swiss currency as the U.S. dollar fell.

Yet even if the government addresses these issues in a way that appeals to Mr. Trump, until Switzerland’s trade deficit with the United States narrows, Swiss goods may face high tariffs for the foreseeable future.