And President Trump and President Xi Jinping of China could meet at the G20 summit in late June in Osaka, Japan, which would be an opportunity for de-escalation at the highest levels.

But open lines of communication and time to work won’t by themselves solve the problem of how to finesse some mutually agreeable deal, particularly given that both countries view this negotiation as resetting their economic relationship in ways that would have long-lasting consequences.

Add in Mr. Trump’s tendency to view every negotiation through a zero-sum prism, and it may be hard to find a pathway for both parties to go home able to proclaim victory.

When the negotiations seemed to be going well a few weeks ago, “I thought we were going toward constructive ambiguity,” said Mary E. Lovely, an economist and trade expert at Syracuse University’s Maxwell School.

The United States is demanding that China codify rules into law to protect American companies (and their technology) that do business in China. Chinese negotiators now reject that possibility; American officials said they had agreed to those provisions.

“It looks like there was a level of specificity that China wasn’t willing to accept and a level of ambiguity that the Trump administration wasn’t willing to accept,” Ms. Lovely said. “It looks like the Chinese are firm that there are some areas where they are not willing to go, that they see as disrespectful.”

If the escalation now being signaled by both sides goes into force, Americans will face higher prices for a wide range of goods, and certain American manufacturers will face less demand for their products. Already, American farmers are suffering amid reduced Chinese demand for soybeans and other products. The Chinese manufacturing sector is hurting as well — and is likely to suffer further if tariffs reduce American demand for their products or drive relocation of production to other countries.