Nearly one year after Donald Trump’s upset election victory, support for the president is eroding in counties that were most responsible for his election, a new Wall Street Journal/NBC News poll finds. But Democrats have not yet managed to turn Mr. Trump’s weakness in those precincts into gains for their party. (See the full results.)

People in these so-called “Trump counties” remain far more likely than the rest of the nation to approve of the president’s job performance and handling of the economy. But disapproval of his...