Even after President Trump announced sweeping global tariffs in April, some investors and supporters comforted themselves by arguing that the president’s goal was still to open global markets, not close them off.

The belief, promoted by Mr. Trump himself, was that he was using his tariffs as a lever to crack open foreign markets and the administration would soon deliver dozens of deals that would increase U.S. exports and help American businesses flourish abroad.

Three months later, that optimism is being replaced by doubts that Mr. Trump’s goal was ever to strike the kind of trade deals that would open up markets. When Mr. Trump paused his global tariffs for 90 days in April, he said the delay would give his administration time to reach trade deals with countries across the world. In the intervening months, Mr. Trump boasted about how countries were lining up to talk to the United States and at one point claimed he had reached 200 deals.

But the administration has only announced two preliminary deals, with Britain and Vietnam, and the status of the Vietnam deal is now in question. While handshake agreements with India, Taiwan and other governments could soon be pending, they are likely to be limited pacts that leave much left to be negotiated. Even when deals have been announced, the administration has left double-digit tariffs in place, with the promise of more levies on foreign products on the way.

On Saturday, Mr. Trump announced in a letter posted to social media that he would place a 30 percent tariff on goods from the European Union and Mexico, starting on Aug. 1. His administration had been in active negotiations with both the E.U., a trading bloc of 27 nations, and Mexico.

The tariffs on Mexico are similar to what Mr. Trump imposed on Canada earlier in the week and come despite the fact that Mr. Trump brokered a trade deal with Mexico and Canada during his first term that was intended to stabilize economic relations between the United States and its neighbors.

The new letter comes after Mr. Trump sent out nearly two dozen letters notifying countries of the high tariff rates they will be charged as of Aug. 1 if they don’t sign trade deals. That included nations that were also in active negotiations with the United States, like Indonesia, South Korea and Malaysia.

With less than a month before the Aug. 1 tariffs kick in, the Trump administration may have the capacity to deal with only a fraction of those countries. Some governments that have sought out meetings with U.S. officials have not been able to schedule them.

Mr. Trump has seemed unbothered by not having more deals to announce. Instead, he has extolled the volume of tariffs he is heaping on America’s trading partners, claiming that they are more than justified and are bringing in huge sums of money to the United States.

“Everybody has to pay and the incentive is that they have the right to deal in the United States. If they don’t want to, they don’t have to pay,” he said during a cabinet meeting on Tuesday.

He acknowledged that his government doesn’t have the capacity to do trade deals with every nation, but also seemed to suggest that the letters he was sending amounted to trade deals.

“We have made some deals,” he said. “We can make a lot more deals. It’s just too time consuming. It just makes it more complicated. And we can do things over the years, too.”

“A letter means a deal,” the president added. “We got 200 countries. We can’t meet with 200 countries.”

Republicans who have long supported free trade, or who come from agricultural states that depend on foreign markets, have argued that, in the hands of a consummate dealmaker, Mr. Trump’s tariffs could be a tool for more active trade.

During a hearing in April, shortly after Mr. Trump had announced his global tariffs, Republican senators expressed dismay about whether trade wars would harm U.S. exporters. They pressed Jamieson Greer, Mr. Trump’s top trade negotiator, on whether tariffs would remain in place in the long run.

Steve Daines, a Republican senator from Montana, said there was “hope that these tariffs are a means and not solely an end.”

Senator Chuck Grassley, a Republican of Iowa, said he had taken a “wait and see” approach to tariffs because he believed Mr. Trump was using them as a tool to get fairer trade. “If that’s not the case, level with me,” he told Mr. Greer.

Stock market investors also appear to have become used to Mr. Trump’s pattern of repeatedly pausing and delaying the most dramatic of his threatened tariffs, seeing them more as a negotiating tool than a concrete economic threat.

But Mr. Trump’s Aug. 1 deadline is closing in and he has insisted he will not delay the global tariffs any longer. With the administration already struggling to land deals with a few major trading partners, the bulk of countries are likely to face significantly high tariffs than they did before.

Ernie Tedeschi, the director of economics at the Budget Lab at Yale University, said that the country’s average effective tariff rate on imported products had gone from just 2.5 percent at the beginning of the year to 18.7 percent, including the tariff letters the president issued last week. That’s the highest average U.S. tariff rate since 1933, on par with the Smoot-Hawley tariff peaks that worsened the Great Depression.

“To me that’s pretty conclusive evidence that he’s a protectionist,” Mr. Tedeschi said. “I think this is an administration that just likes tariffs as a policy.”

Mr. Trump has often referred longingly to the days when William McKinley was president, talking about how his tariffs made America rich.

“He was the tariff king, but he was very, very strong,” Mr. Trump said at Tuesday’s cabinet meeting. “It was an all-tariff country,” he said, adding “we had so much money we didn’t know what to do with it.”

A White House official said that deals and tariffs weren’t mutually exclusive for the Trump administration. For many deals, including the one announced with Britain, higher tariffs have been part of the overall package, along with concessions to open up the foreign market, he said. Many of Mr. Trump’s supporters are happy that he is leaving high tariffs in place, saying they are needed to ensure that the valuable U.S. market is preserved for American companies.

Wendy Cutler, the vice president at the Asia Society Policy Institute, said that Mr. Trump’s policies included an element of opening markets, as well as protectionism. U.S. negotiators are working hard to push other countries to open up their markets, she said. “That’s all about increased access for U.S. exporters. But, let’s be honest, at the same time, we’re putting up high tariffs.”

She also argued that, even if the administration doesn’t strike many deals, it could cover a significant portion of U.S. trade by concentrating on major trading partners. “If indeed deals are announced with India and the E.U. over the next three weeks, that would carry a lot of weight,” she said.

Mr. Trump’s tariffs have clearly created leverage with other trading partners, and dozens of foreign countries have appealed to the White House to try to strike better trade terms. But business leaders have stressed that, so far, the president’s tactics are making it more difficult, rather than easier, for them to do business abroad.

Jake Colvin, the president of the National Foreign Trade Council, which lobbies on behalf of international business, said that it was “shocking how far the center of gravity has moved on the tariff conversation.”

“Back when the president floated the idea of a universal baseline tariff a year ago as a candidate, everyone was aghast at how dramatic that would be,” he said. “And now there’s almost relief by companies and businesses that a 10 percent baseline tariff might be the best they can get.”