Over all, Mr. Biden led Mr. Trump by eight percentage points in Michigan, 48 percent to 40 percent, among likely voters. His lead in Wisconsin was slightly larger, 51 percent to 41 percent.

The new results, along with recent Times/Siena surveys from elsewhere in the Northern battlegrounds, suggest that the president has not yet managed to reassemble his winning coalition across the region. He faces modest but significant defections among white and independent voters, while facing a groundswell of opposition from those who voted for a minor-party candidate or didn’t vote at all in 2016.

The president’s path to re-election is narrow if he doesn’t win either Wisconsin or Michigan. If Mr. Biden puts those two states in his column, along with the states carried by Hillary Clinton in 2016, he will hold 258 electoral votes, putting him on the doorstep of the 270 needed to win.

Nonetheless, the Trump campaign appears to recognize that the two states no longer represent his likeliest path to re-election. Over the last month, the campaign has reduced its television ad spending in the two states in favor of an apparent push to sweep Arizona, Florida and Pennsylvania, where Times/Siena surveys conducted since the first debate show the president trailing by somewhat narrower but still significant five-to-eight-point margins.