He said that polling also showed that most people in Michigan credit Mr. Obama, whose administration bailed out General Motors at the depths of the Great Recession, for helping the auto industry and the thousands of jobs that go with it.

In Wisconsin, 28 percent of registered voters said they would definitely vote for Mr. Trump’s re-election and 14 percent said they probably would, according to a Marquette University Law School survey in April.

In Pennsylvania, a recent Franklin & Marshall College poll found that 36 percent of registered voters favored Mr. Trump’s re-election while 61 percent said it was time for a change, numbers that may be more troubling given that people in the state said they felt economic conditions had improved since 2016, even with job losses in parts of the manufacturing sector.

Another sign that the president might be losing support in Pennsylvania was the victory of Senator Bob Casey, a Democrat, who in November won his third term in the state. Mr. Casey beat his main opponent in the heavily industrialized Erie County, for instance, by 18 points, compared to Mr. Trump who carried the county by a margin of less than two points in 2016.

A central challenge for Democrats in the three states is whether they can effectively make the case that Mr. Trump’s promises were mere sloganeering, and win back those votes.

In Michigan, that will be determined to a great degree by the health of the auto industry. In the Great Recession, the auto industry suffered greatly, forcing General Motors into bankruptcy for a period as thousands of automotive workers in Michigan lost their jobs. That added to their sense of grievance as voters and helped give rise to Mr. Trump’s victory.

In his campaign speech in Dimondale, Mr. Trump said “the Michigan manufacturing sector is a disaster,” and he blamed the Obama administration’s policies for the struggles of the auto industry, even saying that if he were not elected, Mexico would become “the car capital of the world.”