The August cover of Vogue featuring Dr. Jill Biden was released online Monday — four days after the big debate — and brought with it a fresh round of scrutiny over her role as a die-hard campaigner for her husband, who is locked in a nail-biting campaign for re-election.

During much of President Biden’s term, the first lady was a figure of minimal controversy. That began to shift when campaign season heated up. Laura Ingraham of Fox News claimed that Dr. Biden was covering up the president’s unfitness out of her own desire for political power and prestige. Sounding the same theme, The Daily Caller, a right-wing website, began referring to her as “Lady Mac-Biden.”

Dr. Biden took center stage after Mr. Biden struggled to finish his sentences during a dismal debate performance on Thursday against former President Donald J. Trump. Afterward, The New York Times reported that Dr. Biden was the first person he had turned to: “The first lady’s message to him was clear: They’d been counted out before, she was all in, and he — they — would stay in the race.”

On the Vogue cover, Dr. Biden wears a white Ralph Lauren tuxedo dress. She was photographed in the spring by Norman Jean Roy, whose recent contributions to Vogue include portraits of Nicki Minaj, Alicia Keys and the White House press secretary, Karine Jean-Pierre. The accompanying profile of the first lady, by Maya Singer, describes her as a “vision of calm amid utter cacophony.”

Dr. Biden has been on the cover of Vogue twice before. Tina Brown, the former editor of Vanity Fair and The New Yorker, noted that an appearance on the Vogue cover is a “rite of passage” for first ladies. Still, Ms. Brown added, the implications of Dr. Biden’s appearance on the cover of a fashion magazine are “always a risk.” And at this moment, the Vogue cover “is not particularly helpful,” she added.

Soon after the magazine posted the cover image to its Instagram account on Monday, the comments were overwhelmingly negative. Some were from Trump supporters who took Dr. Biden’s appearance as an opportunity to complain about the fact that Melania Trump had been passed over for a Vogue cover when she was first lady. A number of other critical remarks seemed to come from Democrats, one of whom argued that Dr. Biden was pursuing her and her husband’s own ambitions “at the expense of Americans safety and happiness.”

The cover line — “We decide our future” — did not seem to help, regardless of the fact that the first lady seemed to be talking about women voters when she said those words at a Minnesota campaign event in April.

“No!” a commenter wrote. “We decide your future! Done with your entitlement.”

Janice Min, the editor in chief of Ankler Media, who was previously the top editor of The Hollywood Reporter and Us Weekly, concurred.

“It’s not a great look when the president refuses to give news outlets one-on-one interviews but his wife has her third Vogue cover during an election where voters are saying over and over again it is all about the economy,” Ms. Min said. “Is the Vogue audience really the path to victory in Michigan, Wisconsin and Nevada?”

Ms. Min further noted that Vogue is also edited by Anna Wintour, who has hosted private fund-raisers for Mr. Biden’s re-election.

“In an era where trust is in question, and Donald Trump is telling people the system is rigged and people believe him, I have to wonder about the wisdom of speaking through a publication edited by one of Joe Biden’s biggest fund-raisers,” Ms. Min said.

A representative for Vogue and Ms. Wintour said by email: “It’s no secret that Anna has been a supporter of Democratic campaigns for decades. Our August cover story is a look at the tremendous work Dr. Biden has done, and the most urgent issues in 2024 and beyond.” (The spokeswoman did not respond directly to a question for Ms. Wintour about whether she thought Mr. Biden should bow out of the race.)

Vogue did reach out to the first lady for comment after the debate. On the Vogue website, the article has an update at the top saying that Dr. Biden spoke to the magazine from Camp David on Sunday. The Biden campaign, she said, “will not let those 90 minutes define the four years he’s been president. We will continue to fight.” Dr. Biden added that her husband would “always do what’s best for the country.”

Some who read those words on Monday felt Dr. Biden might be hedging about her husband’s decision to remain in the race. Cindi Berger, the chief executive of R&CPMK, one of the entertainment industry’s biggest public relations and crisis management firms, noted that Dr. Biden could have said, but did not say: “The idea of him dropping out is a nonstarter. We are in this to win this and will see the voters at the polls in November.” Instead, Ms. Berger noted, Dr. Biden said the couple “will continue to fight.”

“There’s an opening — that’s how I take it,” said Ms. Berger, a Democrat who called Mr. Biden an “extraordinary and remarkable president” but indicated that she thought the “right thing” would be for him to step aside.

Elizabeth Alexander, the first lady’s communications director, did not comment when asked if there was wiggle room in the Vogue quote.

Ms. Brown, for her part, said she wasn’t reading much into the quote. “I think Jill is all in and not a chance would advise him to step out,” she said via text. “She loves being queen after waiting it out through the hoity-toity Obama circle!”