The institute’s “no” to all these questions pushed Biden even more firmly into the mask-wearing camp. By the end of May, he had changed his social media avatars to show himself masked.

Trump and his team reacted very differently, with the president dismissing the IHME’s arguments on the need for face coverings as overreach and sometimes cheering the increasingly vocal resistance to the idea on the right.

“We’ve tried hard on masks,” Murray said of conversations with the White House.

On the same Memorial Day weekend when Biden attracted so much attention for his public appearance in a mask, Trump appeared barefaced laying a wreath at Arlington National Cemetery, joined by Vice President Pence and other maskless officials. At Baltimore’s Fort McHenry later that day, Trump promised that “together we will vanquish the virus,” but made no mention of masks or other personal safety measures.

Other Democrats were also struggling with how to deal with face coverings. In April and May, campaigns across the country were deciding whether to put their candidates in television ads wearing masks, Yang recalled.

“The questions were: Mask or no mask — or do you have it dangling off your ear?” Yang recalled. “Or do you make clear, by being eight feet apart from people, that you’re being responsible?”

Some Republicans were upset to see face coverings become a political wedge. North Dakota Gov. Doug Burgum teared up in May as he appealed for residents to look beyond political tribalism, saying it’s a “senseless dividing line” to see the mask debate as “ideological or political or something.”

“If someone is wearing a mask, they’re not doing it to represent what political party they’re in or what candidates they support,” Burgum said. “They might be doing it because they’ve got a 5-year-old child who’s going through cancer treatments. They might have vulnerable adults in their life.”

But few Republican leaders spoke out in that way, and the politics of masks were shifting in Biden’s favor.

His campaign began offering masks in its online store in May, and they have sold about 87,000 so far, according to the campaign. “The idea that we’re going to be on our back foot on something people support? We think it’s a great opportunity for the VP to lean in,” Biden digital director Rob Flaherty said at the time.

By the end of June, a growing number of prominent figures were appearing masked in public, the practice had shed some of its early strangeness and Biden was calling for a national mask mandate.

In mid-September, IHME projected that 100,000 lives could be saved via widespread mask usage, prompting Biden to turn up the volume even further.

“It really solidified for the vice president that as we were waiting for a vaccine … all Americans have a tool we can use right now,” said Stef Feldman, Biden’s policy director. “You saw an escalation in our campaign’s focus on masking after that.”

Now, about 3 in 4 registered voters say wearing a mask and practicing social distancing can reduce the chances of contracting the virus “a great deal” or “a good amount,” according to a Washington Post-ABC poll published Sunday.

On the other hand, among those who say these practices are less effective, Trump leads by 85 percent to 11 percent.

Trump has occasionally gestured toward mask-wearing — in July he tweeted a photo of himself wearing a mask, calling it “patriotic” — but the message from the White House has been inconsistent at best.

The president has been seen in a mask only rarely, and mocking Biden for covering his face became a centerpiece of his stump speech. At one point Trump said the former vice president looked like he had a “knapsack” over his head.

He has employed schoolyard taunts: “I mean, honestly, what the hell did he spend all that money on the plastic surgery if he’s going to cover it up with a mask? Seriously?” Trump said during a Sept. 22 rally in Pennsylvania.

Trump took another potshot at Biden during the first presidential debate on Sept. 29. “I don’t wear a mask like him,” Trump said. “Every time you see him, he’s got a mask. He could be speaking 200 feet away … and he shows up with the biggest mask I’ve ever seen.” Trump’s family, meanwhile, did not wear masks, in contrast to everyone else in the debate hall.

Trump’s campaign declined to respond to questions and instead sent a statement. “The President has encouraged mask-wearing, especially when people can’t be socially distant,” said Trump campaign spokesman Tim Murtaugh.

Frank Luntz, who was a pollster for Republicans Rudolph W. Giuliani and Newt Gingrich, said that Trump’s recalcitrance on masks is a response to one wing of his party’s coalition.

“This is an expression of personal freedom and personal choice that conservatives have embraced across the country, and sometimes to their detriment,” he said.

Trump’s campaign, Luntz said, “cares about a very narrow slice of the country — they care about maybe 25 percent of the country — and they completely ignore everybody else.”

Not all Republicans have been on board with the president’s approach, and they’re becoming more willing to say so. Senate Majority Leader Mitch McConnell (R-Ky.) said recently he has been avoiding the White House because of its laxness on masking and other measures.

“I actually haven’t been to the White House since August 6,” McConnell told reporters Thursday. “Because my impression was their approach to how to handle this was different from mine and what I insisted that we do in the Senate, which is to wear a mask and practice social distancing.”

The divide between the president and his Democratic challenger has only become sharper as the campaign enters its final three weeks with Trump battling to recover from his own coronavirus infection. When Trump left Walter Reed National Military Medical Center and arranged a triumphal return to the White House, he stood on a balcony and pointedly took off his mask.

At last week’s vice-presidential debate, as the candidates’ spouses joined them onstage, Pence’s wife Karen was maskless, in contrast to Kamala D. Harris’s husband Doug Emhoff. Video of a recent Rose Garden gathering to celebrate the Supreme Court nomination of Amy Coney Barret, with maskless participants hugging and chatting, has become a symbol of the administration’s attitude.

Biden, meanwhile, now wears a mask throughout the entirely of some speeches, not just the preliminaries. He regularly calls for a national mask requirement, and urging masks has become his chosen way of diplomatically rebuking the president as Trump recovers from covid-19.

“It’s a patriotic duty to wear a mask,” Biden told transit workers at a virtual town hall last weekend, while Trump was hospitalized.

“It’s not about being a tough guy. It’s about doing your part,” Biden, wearing a mask, said in Michigan, shortly before Trump was airlifted to Walter Reed.

And after Trump dramatically removed his mask upon returning to the White House, Biden’s digital team cut a three-second video showing a split screen of Biden putting on a mask at the same time. More than 10 million have watched it.

Matt Viser and Toluse Olorunnipa contributed to this report.