WASHINGTON — The disclosure that President Trump paid little or no federal income taxes for years, including while in the White House, convulsed the presidential campaign on Monday with only five weeks to go and immediately scrambled the equation and stakes of the first debate to be held on Tuesday night.

While Mr. Trump tried to deflect the news about his taxes, and his Republican allies generally kept their silence, Democrats pounced and former Vice President Joseph R. Biden Jr., the party’s presidential candidate, posted a video noting that the president paid less in income taxes than everyday Americans like teachers, firefighters and nurses.

The report in The New York Times, published online on Sunday evening and in print on Monday, revealed that Mr. Trump paid no federal income taxes for 11 of the 18 years examined and just $750 in 2016, the year he won the presidency, and $750 in 2017, his first year in office. Mr. Trump wrote off more than $70,000 paid to style his hair during “The Apprentice” and collected $72.9 million in refunds challenged by I.R.S. auditors. He owes hundreds of millions of dollars due in the next four years.

The tax data analyzed by The Times, which was provided by sources with legal access to it, further undercut the image of a wildly successful businessman long projected by Mr. Trump while he was reporting expansive and chronic losses by many of his marquee properties like his golf courses in Florida and Europe and his hotel in Washington — losses that he then used to reduce or eliminate tax liabilities.

How the revelations may change the presidential campaign was an open question. The race has remained remarkably steady and without major shifts through all sorts of seismic developments. But with only 35 days before the election on Nov. 3, every day that the president does not transform the dynamics of a campaign that polls show he is currently trailing in is a missed opportunity.

“We know the vast majority of Americans long ago made up their minds about President Trump, either for or against him, so the tax revelations are not likely to shift the election in any fundamental way,” said Whit Ayres, a Republican pollster. “That said, they could play a role in giving Joe Biden some ammunition for the debate and at the margins for some people who feel that $750 is not enough to pay in taxes regardless of the circumstances.”

Mr. Trump, who unlike other presidents since Watergate has adamantly refused to release his tax returns and fought efforts to obtain them all the way to the Supreme Court, attacked the Times report on Monday on Twitter without actually denying any of its particulars.

“The Fake News Media, just like Election time 2016, is bringing up my Taxes & all sorts of other nonsense with illegally obtained information & only bad intent,” he wrote. “I paid many millions of dollars in taxes but was entitled, like everyone else, to depreciation & tax credits.” He later refused to take questions at his only public event of the day.

But there was quiet concern within the campaign, where aides took note of daily tracking numbers from Rasmussen Reports, a typically rosy assessment of how the president is faring, that showed support falling after the tax story. Among Mr. Trump’s circle, there was finger-pointing about how the issue was handled and a hesitancy to discuss with him an issue they know he is sensitive about.

Many of the president’s advisers argued that such stories have never harmed his standing with core supporters in the past and that this would be no exception. They recognized, however, that Mr. Trump would have to have an effective response prepared for the debate, the first encounter between the two candidates, scheduled for 9 p.m. Eastern at Case Western Reserve University in Cleveland. Some aides suggested he try to finesse an answer similar to what he has said previously, that taking advantage of the tax code is simply “smart” for a business person, while also painting himself as a jobs creator.

Tim Murtaugh, the campaign spokesman, called the report inaccurate because the president has paid “tens of millions in taxes,” without specifying whether they were federal income taxes or directly denying that there were years he paid none. “This has been litigated in front of the voters before,” he said on Fox News. “The president released more than 100 pages of financial records. And Americans made their judgment in 2016 and elected him president. There’s nothing in there that changes anyone’s mind.”

Still, some of the details, particularly paying only $750 in federal income taxes two years in a row and deducting hairstyling expenses, among other things, could resonate in a visceral way. Democrats expressed hope that they could fuel a sense of injustice with everyday Americans who pay far more themselves and cannot write off hair expenses.

Representative Alexandria Ocasio-Cortez of New York tweeted that she paid thousands of dollars in federal taxes in 2016 and 2017 — when she was still working as a bartender in New York City. “He contributed less to funding our communities than waitresses & undocumented immigrants,” she wrote. The Biden campaign video showing the typical income tax paid by various workers amplified the attack.

The Biden campaign also began selling T-shirts, buttons and stickers that say, “I paid more income taxes than Donald Trump.” And the campaign on Monday launched an online “Trump tax calculator” allowing people to calculate how much more they paid in federal income taxes than Mr. Trump. “Mad? Us too,” the web page for the tax calculator said. “Join our campaign to elect Joe Biden and make ‘billionaires’ like Donald Trump pay their fair share.”

In an interview with MSNBC, she said the president owed full disclosure. “The American people have a right to know that when the president of the United States acts, he acts with their priorities in mind, not with his priorities in mind,” she said. “And we’ve already known that he puts his political priorities in front of the American people.”

The records reviewed by The Times showed that Mr. Trump was personally responsible for loans and other debts totaling $421 million, with about $300 million of it coming due in the next four years when he would be serving a second term if he wins on Nov. 3. That raised the scenario of lenders being forced to decide whether to foreclose on a sitting president or give him a special break to avoid doing so.

“This president appears to have over $400 million in debt, 420, whatever it is, million dollars in debt,” Speaker Nancy Pelosi said on MSNBC. “To whom? Different countries? What is the leverage they have? So for me, this is a national security question.”

While Republican lawmakers dodged questions about Mr. Trump’s taxes, John Kasich, the Republican former governor of Ohio who has endorsed Mr. Biden, said the disclosures could affect blue-collar voters who are not yet decided.

“These folks are scraping to make a living and they’re going to wake up to find out this incredible mogul paid $750? I don’t care what his excuses are,” Mr. Kasich told CNN. “It doesn’t pass the smell test. It’s not going to disrupt those people who were for him totally. They’ll still be for him. But it’s those people on the fence.”

Senator Charles E. Grassley of Iowa, the chairman of the Senate Finance Committee that writes tax law, declined to comment on how little Mr. Trump paid in taxes. “The thought that comes to my mind is how come it’s taking the I.R.S. so long to get the audits done,” he told reporters. Asked about the $750 tax payments, Mr. Grassley said, “I want to wait until the I.R.S. gets done so I know how much he owes.”

Other Republicans avoided discussing the matter at all. Spokesmen for Senator Mitch McConnell of Kentucky and Senator John Thune of South Dakota, the top two Republicans in the Senate, declined to comment.

One of the few prominent voices outside Mr. Trump’s campaign to come to his defense was Rush Limbaugh, the conservative talk show host who received the Presidential Medal of Freedom in February at Mr. Trump’s State of the Union address.

Mr. Limbaugh said on his show on Monday that Mr. Trump’s penchant for minimizing his taxes was something to be proud of, not scorned. “He’s a master at this,” Mr. Limbaugh said. “These tax returns show that he is a master at using the tax code legally. If Trump had done all of this illegal stuff after all of these years, it would have caught up with him by now.”

Mr. Trump on Sunday night initially dismissed the Times report as “fake news” only to pivot on Monday to say that it was information that was illegally obtained.

Dean Baquet, The Times’s executive editor, wrote in an editor’s note published Sunday that “the Supreme Court has repeatedly ruled that the First Amendment allows the press to publish newsworthy information that was legally obtained by reporters even when those in power fight to keep it hidden.”

In his tweets, the president seemed to be as upset about the perception that he is not as wealthy and successful as he claims to be.

“If you look at the extraordinary assets owned by me, which the Fake News hasn’t, I am extremely under leveraged — I have very little debt compared to the value of assets,” he insisted. Mr. Trump said he might release a new financial document. “It is a very IMPRESSIVE Statement, and also shows that I am the only President on record to give up my yearly $400,000 plus Presidential Salary!”

In fact, as the article noted, Mr. Trump is heavily in debt, and much of what he owes to lenders will have to be paid back in just a few years. Mr. Trump is not the only president to give up his salary; Herbert Hoover and John F. Kennedy did, too. But Mr. Trump’s company has been paid hundreds of thousands of dollars by the government in compensation for rooms at his properties for Secret Service and staff members.

Reporting was contributed by Maggie Haberman, Shane Goldmacher and Neil Vigdor from New York, and Nicholas Fandos, Thomas Kaplan, Annie Karni and Zach Montague from Washington.