PHOENIX — Cindy Bishop is the sort of voter who has some Republicans bracing for a wipeout next month.
Standing inside her garage, shielded from the 102-degree desert heat, Ms. Bishop, a 61-year-old medical professional, said she voted for Mr. Trump four years ago because “he wasn’t a politician.” But then, she said, “I got a taste of him and I’m like, ‘God, he’s disrespectful’ — there’s so much about him I don’t like.” She is now leaning toward Joseph R. Biden Jr.
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.
“There are limits to what people can take with the irresponsibility, the untruthfulness, just the whole persona,” said Jeff Flake, the former Republican senator from Arizona. Mr. Flake is crossing party lines to support Mr. Biden, who made his first visit of the general election here Thursday.
Many of the Sun Belt states seemingly within Mr. Biden’s reach resisted the most stringent public-health policies to battle the coronavirus. As a result, states like Arizona, Georgia and Texas faced a powerful wave of infections for much of the summer, setting back efforts to revive commercial activity.
In Arizona, a low-tax, regulation-resistant state, the focus on reviving business helped drive the unemployment rate down to 5.9 percent in August, with some of that apparent improvement coming from people leaving the labor force in a state with a large hospitality sector that has suffered in the pandemic.
Still, Arizona continues to face a long climb to return to its pre-pandemic economy. Twice as many Arizona residents filed new claims for unemployment benefits at the end of September than they did at the previous time last year, the Labor Department reports.
Mr. Biden is mounting an assertive campaign and facing rising pressure to do more in the historically Republican region. He is buttressed by a fund-raising gusher for Democratic candidates, overwhelming support from people of color and defections from the G.O.P. among college-educated whites in and around cities like Atlanta, Houston and Phoenix.
“Cities in states like Arizona and Texas are attracting young people, highly-educated people, and people of color — all groups that the national Republican Party has walked away from the last four years,” said the Oklahoma City mayor, David F. Holt, a Republican. “This losing demographic bet against big cities and their residents is putting Sun Belt states in play.”
Gov. Doug Ducey of Arizona, a Republican who like Mr. Holt has won in increasingly forbidding environments, said his party needed to recognize an enduring verity about politics: “It’s a game of addition.”
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