Mr. Trump’s vulnerability even in conservative-leaning states underscores just how precarious his political position is, less than six weeks before Election Day. While he and Mr. Biden are competing aggressively for traditional swing states like Wisconsin, Pennsylvania and Florida, the poll suggests that Mr. Biden has assembled a coalition formidable enough to jeopardize Mr. Trump even in historically Republican parts of the South and Midwest.

A yawning gender gap in all three states is working in Mr. Biden’s favor, with the former vice president making inroads into conservative territory with strong support from women. In Iowa, where Mr. Biden is ahead of Mr. Trump, 45 percent to 42 percent, he is up among women by 14 percentage points. Men favor Mr. Trump by eight points.

In Georgia, where the two candidates are tied at 45 percent, Mr. Biden leads among women by 10 points. Mr. Trump is ahead with men by a similar margin of 11 percentage points.

Mr. Trump’s large advantage among men in Texas is enough to give him a small advantage there, 46 percent to 43 percent.