It isn’t clear how much Mr. Trump’s trade policies will matter in next year’s election. Trade hasn’t historically been decisive in presidential races, and it ranks low among the issues that voters are focused on. It is also difficult for Democrats to capitalize on the issue because several of their leading presidential candidates, including Senators Elizabeth Warren and Bernie Sanders, are also skeptical about trade agreements. The issue barely came up at the first Democratic presidential debates on Wednesday and Thursday evenings.

“People don’t think about trade a lot,” said Carroll Doherty, director of political research for the Pew Research Center. “It’s a pretty low-priority issue.”

That could change, Mr. Doherty said, if the trade war starts to damage the broader American economy, costing more people like Ms. Frandsen their jobs. There isn’t much evidence of that so far — economic growth was solid in the first three months of the year, and the unemployment rate is at a nearly 50-year low. But growth has been slowing, and businesses are increasingly warning that tariffs are taking a toll.

“A lot of it depends on events and what happens over the next six months,” Mr. Doherty said.

There are signs that Americans are starting to pay more attention. More than two-thirds of those polled — and more than half of Republicans — said they believed that Mr. Trump’s trade policies would cause prices to rise. That is a break from past surveys, in which fewer people drew a link between tariffs and prices, said Alexandra Guisinger, a Temple University political scientist who wrote a book about public opinion on trade. She said the shift could reflect increased media coverage of trade and efforts by business groups and others to influence sentiment.

“That recognition that tariffs are something that consumers would pay is something that’s new,” Ms. Guisinger said.