The latest Wall Street Journal/NBC News poll found signs that President Donald Trump’s support is eroding in important segments of his base: white Americans without a four-year college education and self-described white working-class voters.

Mr. Trump won the non-degree group by more than 30 percentage points in the 2016 election, making it a core source of support. In the new poll, his job approval dropped 7 points in that group, falling to 51% in October from 58% in September. Among self-described white working-class respondents, Mr. Trump’s approval rating fell 12 points, to 41% from 53%.

Overall, Mr. Trump’s job approval dropped 5 points to 38% in the poll, which was conducted Oct. 23-26.

Those drops occurred during a period when Mr. Trump’s job-approval numbers among other groups—such as middle- and upper-income voters and college graduates—were essentially unchanged between September and October.

The groups that eased away from the president in October have a special significance to him. Much of Mr. Trump’s messaging has been aimed at those who feel as if they have been left behind economically, such as the country’s manufacturing workers.