The inflammatory behavior that has alienated voters beyond his base has long posed the most significant impediment to Mr. Trump’s re-election. But one week after he rampaged through the first presidential debate and then was hospitalized with the coronavirus, only to keep minimizing the disease as it spread through his White House, the president’s conduct is not only undermining his own campaign but threatening his entire party.

New polls show Mr. Trump’s support is collapsing nationally, as he alienates women, seniors and suburbanites. He is trailing not just in must-win battlegrounds but according to private G.O.P. surveys, he is repelling independents to the point where Mr. Biden has drawn closer in solidly red states, including Montana, Kansas and Missouri, people briefed on the data said.

Nowhere has Mr. Trump harmed himself and his party more than across the Sun Belt, where the electoral coalition that secured a generation of Republican dominance is in danger of coming apart.