WASHINGTON—President Trump’s standing among Americans remained effectively unchanged even as he presided over the longest partial government shutdown in U.S. history, the latest example of how his unusual brand of politics has resonated with a strong core of supporters.

Mr. Trump’s approval rating was at 43% in a new Wall Street Journal/NBC News poll, with 54% disapproving of his job performance. That was the same mark as in a December survey taken 10 days before the start of the shutdown. The latest survey was conducted...