Donald Trump has stepped up his propaganda against the F.B.I., the Justice Department, and the special counsel, Robert Mueller. In a series of tweets on Tuesday, he returned to the claim that the F.B.I. had spied on his election campaign. Then he introduced a new angle, claiming, “The 13 Angry Democrats (plus people who worked 8 years for Obama) working on the rigged Russia Witch Hunt, will be MEDDLING with the mid-term elections, especially now that Republicans (stay tough!) are taking the lead in Polls.”

It didn’t take long for media outlets including the Washington Post and CNN to put up pieces debunking Trump’s claim and labelling it yet another conspiracy theory with no basis in fact, but Trump doesn’t care about that. Propaganda isn’t meant to be true; it is meant to shift the opinions of a target audience, which in this case consists of Republicans, and, to a lesser extent, independent voters.

For weeks now, Trump and his sidekicks—Rudy Giuliani, Devin Nunes, Mark Meadows, and other Republicans who should know better—have been engaged in a concerted effort to discredit Mueller’s investigation. As Dan Balz, the veteran Washington Post columnist, pointed out a few days ago, there is disturbing evidence that this campaign is working. Among Republican voters particularly, support for allowing Mueller to complete his investigation has fallen significantly. These developments raise two questions: Why is Trump’s strategy working? And can anything be done to counter it?

Trump’s skills as a propagandist shouldn’t be underestimated. Even before he entered politics, he had spent decades trying to manipulate the news media to his advantage. By instinct or design, his attack on Mueller meets many of the requirements for a successful misinformation campaign that the British author A. J. Mackenzie listed in his 1938 book, “Propaganda Boom”: repetition; a catchy slogan; color; a specific objective; a kernel of truth; concealment; and timing.

The kernel of truth is that the F.B.I. did use an informant in 2016 to approach certain figures in the Trump campaign who were suspected of having ties to Russia. The use of informants is standard practice in counterintelligence investigations, but Trump immediately branded this informant a “spy.” According to a story by the Associated Press, he believed “the more nefarious term would resonate more in the media and with the public.”

Having seen “spy” and “Spygate,” another of his creations, repeated countless times in news stories and on television broadcasts, Trump is now trying to replicate the trick with “13 Angry Democrats,” which refers to reports that thirteen members of Mueller’s legal team were, at one point, registered as Democrats. The goal is to portray the investigation as a partisan venture, and, therefore, an illegitimate one. (Trump doesn’t mention the fact that Mueller is a lifelong Republican and so is Rod Rosenstein, the Deputy Attorney General, who is overseeing the investigation.)

Repetition is key to the Trump strategy. Practically every day, he attacks the Mueller investigation on Twitter. Giuliani, meanwhile, is busy using more traditional platforms to spread the message. On Tuesday, he told the Washington Post that Trump wouldn’t sit for an interview with Mueller unless the special counsel allowed the President’s legal team to review all the documents relating to the F.B.I.’s use of an informant in 2016. (The Post’s story noted that Giuliani used the term “Spygate.”)

The one item on Mackenzie’s list that is lacking in Trump’s strategy is concealment. When CNN’s Dana Bash asked Giuliani on Sunday about the President’s attacks on Mueller, he replied, “It is for public opinion, because eventually the decision here is going to be impeach or not impeach. Members of Congress—Democrats and Republicans—are going to be informed a lot by their constituents. And so our jury, and it should be, is the American people.”

You might think that such a comment would undermine the effectiveness of Trump’s propaganda campaign by exposing its true objective. Alas, no. In our highly polarized political system, there are plenty of conservative media outlets eager to parrot Trump’s claims, however contrived they are, and plenty of people willing to listen to them, even as fact-based media outlets continue to point out the lack of supporting evidence.

“The bad news is that people tend to engage in directionally motivated reasoning,” Brendan Nyhan, a political scientist at Dartmouth who is an expert on how people assimilate political information, told me on Tuesday. Directionally motivated reasoning is what happens when people confronted with conflicting views on controversial issues, even purely factual ones, tend to believe the source they perceive to be on their side, Nyhan said. In experiments with students and other participants, Nyhan and his colleagues found that, in some instances, pointing out to people the factual errors in their views can actually be counterproductive: they tend to double down on their beliefs.

According to Nyhan, this helps explain why things like the Obama birther myth and the belief that Iraq had weapons of mass destruction persist, many years after they have been discredited. Fortunately, not everyone is hopeless. In a recent experiment, Nyhan and his colleagues took the alarmist speech that Trump delivered at the 2016 Republican National Convention and explained to a group of people, some of whom were Trump supporters, how Trump’s claim of rising crime rates was simply wrong. “It did seem to change their view of the facts,” Nyhan said. But, he added, “People did not come to view (Trump) more negatively, over all.”

Findings like these highlight why it remains important for serious media outlets to pick apart Trump’s daily fabrications and lies. Exposure to corrective information—particularly repeated exposure—can cause some people to change their minds. But this process can’t be relied on to correct the problem of directionally motivated reasoning, and that’s why it’s also imperative that senior Republicans stand up and defend Mueller and his investigation. “The basic problem is that people take cues from political élites on their side,” Nyhan said. “And right now the cues that Republicans are getting are mostly from Trump. There are very few Republicans defending the rule of law, and that is very worrying.”

Far from questioning Trump’s “Spygate” narrative, some senior G.O.P. figures are validating his tactics. In an interview with the Times, John Cornyn, the second-ranking Republican in the Senate, said that, although he wouldn’t use the President’s exact words, it was legitimate to question the F.B.I.’s “motivation” in launching its investigation of Trump’s Presidential campaign.

Let’s be clear about what’s happening here: acting either out of fear or cynical self-interest, the leadership of the Republican Party is allowing Trump to deliberately defame and undermine law-enforcement agencies that are supposed to operate independently of him, especially on matters related to his conduct. Down this road lies a stunted democracy. History shows that propaganda can be hideously effective, especially when used repeatedly by people in power. (“The past was alterable,” Orwell noted, in “1984.” “Oceania was at war with Eastasia. Oceania had always been at war with Eastasia.”) To overcome these tactics, leaders of influence and authority must confront them with rival narratives based on facts. In this case, the narrative is straightforward: the F.B.I. was just doing its job in 2016, and by keeping secret its investigation of Trump’s campaign it may have helped him to get elected.

So far, the only prominent Republican who has come close to admitting this publicly is Trey Gowdy, the South Carolina representative who is retiring from Congress this year. “When the F.B.I. comes into contact with information about what a foreign government may be doing in our election cycle, I think they have an obligation to run it out,” Gowdy told CBS’s “This Morning,” on Wednesday. That was a welcome development. But don’t hold your breath for Republicans who aren’t retiring to echo Gowdy’s comments.