In the unlikely yet profound showdown between the president and the migrant that has captured international attention, the courts have uniformly determined that one of them recently violated the law. And it wasn’t the migrant.

According to liberal and conservative judges all the way up to the Supreme Court, President Trump’s administration broke the rules by deporting Kilmar Armando Abrego Garcia and must try to fix the mistake. But Mr. Trump and his team are trying to rewrite the narrative so that it is a dispute about illegal immigration rather than the rule of law.

It is a fight that Mr. Trump seems to welcome. His administration could easily have avoided it by simply bringing Mr. Abrego Garcia back from El Salvador and following a process that might have resulted in him being deported anyway. Instead, Mr. Trump opted to double down, defying the courts and reverse-engineering a justification for a deportation that his administration initially acknowledged was wrong.

This in the view of the president’s team is a political winner with the vast majority of voters, an “80-20 issue,” as his adviser Stephen Miller puts it, referring to theoretical percentages. Mr. Trump bolsters his credentials as a scourge of evil immigrants while asserting that his critics care more about foreign-born murderers and thugs than they do about law-abiding Americans. Yet at a time when Mr. Trump is claiming unprecedented power in so many arenas, the case of one imprisoned migrant has come to crystallize the debate about whether Mr. Trump himself is a law-abiding American.

The president’s goal in recent days has been to present Mr. Abrego Garcia as such a dangerous man that it does not matter if the government’s deportation was illegal, in effect arguing that the ends justify the means. Never mind that Mr. Abrego Garcia has never been convicted of a crime, the White House now portrays him as a singular threat to public safety without bothering to prove anything in a court of law.

At a session with reporters on Friday, aides handed Mr. Trump a sheet with bullet points listing various allegations against Mr. Abrego Garcia, some of them rooted in fact and some of them distorted. He is a “foreign terrorist,” Mr. Trump alleged, and “not a very innocent guy,” someone whose “record is unbelievably bad.”

“They talk about how evil I am, that this man would be thrown out of our country,” Mr. Trump said of his critics. “This man is a — according to certified statements that we get — is a very violent person. And they want this man to be brought back into this country, where he can be free.”

He then went on to cite a “wonderful angel mom” whose daughter was killed by an immigrant in the country illegally. The White House made a point of highlighting her case this week by bringing her to the briefing room amid the dispute over what to do about Mr. Abrego Garcia. But her family’s tragedy, which was unquestionably horrific and devastating, was unrelated to Mr. Abrego Garcia, who had nothing to do with it, even though the president essentially seemed to conflate the matters.

“Donald Trump is desperately trying to change the conversation on Kilmar Abrego Garcia’s abduction and disappearance because he’s losing in the courts and in the court of public opinion,” said Kica Matos, president of the National Immigration Law Center. “The vast majority of Americans value the rule of law and the separation of powers, and the public is viscerally responding to these growing attacks on our democracy.”

This case has resonated more broadly, according to some critics of the president, in part because Mr. Trump has made clear that he respects few limits on his power. In recent days, Mr. Trump, who is himself a convicted felon, has gone so far as to say that he is contemplating sending violent criminals who are American citizens to be locked up in El Salvador, where prisons are not governed by minimal U.S. standards.

“Whatever the merits of this individual case, it’s becoming clearer to the American public that he could be any of us,” said Cecilia Muñoz, a former domestic policy adviser to President Barack Obama. “The president is going way too far, further than what he told the public he would do during the campaign and way farther than what the country is comfortable with.”

Some Democrats have sought to highlight the case, most notably Senator Chris Van Hollen of Maryland, where Mr. Abrego Garcia worked in construction and lived with his wife, a U.S. citizen, and their three children with special needs. Mr. Van Hollen flew to El Salvador this week to meet with Mr. Abrego Garcia.

“If you want to make claims about Mr. Abrego Garcia and MS-13,” the gang, “you should present them in the court, not over social media, not at press conferences, where you just rattle stuff off,” Mr. Van Hollen said after landing at Washington Dulles International Airport on Friday.

Mr. Trump blasted Mr. Van Hollen as “a fool” and a “grandstander.” The president’s ally, President Nayib Bukele of El Salvador, tried to discredit Mr. Van Hollen by posting pictures of the visit, claiming that the senator and the imprisoned migrant were “sipping margaritas” at their meeting.

Mr. Van Hollen said that government officials put the drinks in front of them and that neither of them touched the drinks. “It’s the lengths that President Bukele will go to deceive people about what’s going on,” he said.

Nonetheless, some Democrats are nervous that they are playing into Mr. Trump’s hands by focusing on the case, allowing the president to draw attention away from the market-plunging consequences of his global trade war and other issues that might be more meaningful to many Americans.

“This is the distraction of the day,” Gov. Gavin Newsom of California, a Democrat, said this week when asked about the case during an event he called to focus on Mr. Trump’s tariffs. “This is the debate they want.” He added that Democrats look like they are “defending MS-13” and “someone who’s out of sight, out of mind in El Salvador.”

Defending the rule of law can be politically complicated because it often involves individuals with less-than-perfect histories who, under the American system, are still afforded due process. Mr. Abrego Garcia did come into the United States illegally in 2011 and was arrested in 2019. Two judges accepted the authorities’ claim that he was a member of MS-13, although his lawyers have pointed out that publicly provided evidence against him is circumstantial, like his tattoos or the Chicago Bulls hat he was wearing.

Moreover, his wife, Jennifer Vasquez Sura, filed a request for a protective order against him in 2021, citing violence against her. In a statement this week, she said she did so “in case things escalated” but “things did not escalate” and added that she did not follow through with the process, instead working out their difficulties “privately as a family, including by going to counseling.” She has been publicly campaigning for his release.

As part of the effort to paint Mr. Abrego Garcia as a villain not a victim, the Department of Homeland Security on Friday released what it called a “bombshell investigative report” suggesting that he was a “suspected human trafficker.” It based that on a 2022 episode when he was stopped for speeding in Tennessee with eight other people in his vehicle. But he was not charged with human trafficking and instead simply given a warning for driving with an expired license.

“The media’s sympathetic narrative about this criminal illegal gang member has completely fallen apart,” Tricia McLaughlin, an assistant homeland security secretary, said in a statement. “We hear far too much about the gang members and criminals’ false sob stories and not enough about their victims.”

Mr. Abrego Garcia was never charged with being a gang member or any other crime, and a judge in his 2019 case issued a “withholding of removal” order forbidding him from being deported to his home country of El Salvador because of established fears of endangerment. He was nonetheless sent to a prison there in March in what the Trump administration called an “administrative error.”

The Supreme Court ordered the Trump administration to “facilitate” his return from El Salvador, but the president and his team have indicated they plan to take no action to do so. The case has troubled not just liberal opponents of the president but a number of prominent conservatives, including writers for National Review and the Wall Street Journal editorial page.

Among them is Judge J. Harvie Wilkinson III of the U.S. Court of Appeals for the Fourth Circuit, who issued a searing opinion against the Trump administration on Thursday. Judge Wilkinson, a Ronald Reagan appointee, has been a conservative stalwart for decades, once considered a finalist for the Supreme Court by President George W. Bush.

In his opinion for a unanimous three-judge panel, Judge Wilkinson chastised the Trump administration for asserting that it can “stash away residents of this country in foreign prisons” without due process. “This should be shocking not only to judges, but to the intuitive sense of liberty that Americans far removed from courthouses still hold dear,” he wrote.

Still, Mr. Trump was undaunted. Inveighing against judges has become almost as appealing to him as inveighing against immigrants. Rather than back down, he made clear on Friday that he plans to dig in on Mr. Abrego Garcia’s wrongful imprisonment and will keep taking his case to the public.

“I’m sure it’s a winner politically,” Jack L. Goldsmith, a former assistant attorney general under Mr. Bush, said of the White House argument.

But “the point is the government is bound by the rule of law,” he said. “And it’s just vitally important that in insisting that others — including immigrants — follow the rule of law and court decisions that the government do the same.”