Antonio Mugica was in Boca Raton when an American presidential election really melted down in 2000, and he watched with shocked fascination as local government officials argued over hanging chads and butterfly ballots.

It was so bad, so incompetent, that Mr. Mugica, a young Venezuelan software engineer, decided to shift the focus of his digital security company, Smartmatic, which had been working for banks. It would offer its services to what would obviously be a growth industry: electronic voting machines. He began building a global company that ultimately provided voting machinery and software for elections from Brazil to Belgium and his native Venezuela. He even acquired an American company, then called Sequoia.

Last month, Mr. Mugica initially took it in stride when his company’s name started popping up in grief-addled Trump supporters’ wild conspiracy theories about the election.

“Of course I was surprised, but at the same time, it was pretty clear that these people were trying to discredit the election and they were throwing out 25 conspiracy theories in parallel,” he told me in an interview last week from Barbados, where his company has an office. “I thought it was so absurd that it was not going to have legs.”

But by Nov. 14, he knew he had a problem. That’s when Rudy Giuliani, serving as the president’s lawyer, suggested that one voting company, Dominion Voting Systems, had a sinister connection to vote counts in “Michigan, Arizona and Georgia and other states.” Mr. Giuliani declared on Twitter that the company “was a front for SMARTMATIC, who was really doing the computing. Look up SMARTMATIC and tweet me what you think?”

Soon his company, and a competitor, Dominion — which sells its services to about 1,900 of the county governments that administer elections across America — were at the center of Mr. Giuliani’s and Sidney Powell’s theories, and on the tongues of commentators on Fox News and its farther-right rivals, Newsmax and One America News.

“Sidney Powell is out there saying that states like Texas, they turned away from Dominion machines, because really there’s only one reason why you buy a Dominion machine and you buy this Smartmatic software, so you can easily change votes,” the Newsmax host Chris Salcedo said in one typical mash-up on Nov. 18. Maria Bartiromo of Fox Business reported on Nov. 15 that “one source says that the key point to understand is that the Smartmatic system has a backdoor.”

Here’s the thing: Smartmatic wasn’t even used in the contested states. The company, now a major global player with over 300 employees, pulled out of the United States in 2007 after a controversy over its founders’ Venezuelan roots, and its only involvement this November was with a contract to help Los Angeles County run its election.

In an era of brazen political lies, Mr. Mugica has emerged as an unlikely figure with the power to put the genie back in the bottle. Last week, his lawyer sent scathing letters to the Fox News Channel, Newsmax and OAN demanding that they immediately, forcefully clear his company’s name — and that they retain documents for a planned defamation lawsuit. He has, legal experts say, an unusually strong case. And his new lawyer is J. Erik Connolly, who not coincidentally won the largest settlement in the history of American media defamation in 2017, at least $177 million, for a beef producer whose “lean finely textured beef” was described by ABC News as “pink slime.”

Now, Mr. Connolly’s target is a kind of red slime, the stream of preposterous lies coming from the White House and Republican officials around the country.

“We’ve gotten to this point where there’s so much falsity that is being spread on certain platforms, and you may need an occasion where you send a message, and that’s what punitive damages can do in a case like this,” Mr. Connolly said.

Mr. Mugica isn’t the only potential plaintiff. Dominion Voting Systems has hired another high-powered libel lawyer, Tom Clare, who has threatened legal action against Ms. Powell and the Trump campaign. Mr. Clare said in an emailed statement that “we are moving forward on the basis that she will not retract those false statements and that it will be necessary for Dominion to take aggressive legal action, both against Ms. Powell and the many others who have enabled and amplified her campaign of defamation by spreading damaging falsehoods about Dominion.”

These are legal threats any company, even a giant like Fox Corporation, would take seriously. And they could be fatal to the dream of a new “Trump TV,” a giant new media company in the president’s image, and perhaps contributing to his bottom line. Newsmax and OAN would each like to become that, and are both burning money to steal ratings from Fox, executives from both companies have acknowledged. They will need to raise significantly more money, or to sell quickly to investors, to build a Fox-style multibillion-dollar empire. But outstanding litigation with the potential of an enormous verdict will be enough to scare away most buyers.

And so Newsmax and OAN appear likely to face the same fate as so many of President Trump’s sycophants, who have watched him lie with impunity and imitated him — only to find that he’s the only one who can really get away with it. Mr. Trump benefits from presidential immunity, but also he has an experienced fabulist’s sense of where the legal red lines are, something his allies often lack. Three of his close aides were convicted of lying, and Michael Cohen served more than a year in prison. (Trump pardoned Michael Flynn and commuted the sentence of Roger Stone.)

OAN and Newsmax have been avidly hyping Mr. Trump’s bogus election claims. OAN has even been trying to get to Newsmax’s right, by continuing to reject Joe Biden’s status as president-elect. But their own roles in propagating that lie could destroy their businesses if Mr. Mugica sues.

The letters written by lawyers for Smartmatic and Dominion are “extremely powerful,” said Floyd Abrams, one of the country’s most prominent First Amendment lawyers, in an email to The New York Times. “The repeated accusations against both companies are plainly defamatory and surely have done enormous reputational and financial harm to both.”

Mr. Abrams noted that “truth is always a defense” and that, failing that, the networks may defend themselves by saying they didn’t know the charges were false, while Ms. Powell may say she was simply describing legal filings.

“It is far too early to predict how the cases, if commenced, will end,” he said. “But it is not too early to say that they would be highly dangerous to those sued.”

Lawyers said they expected that the right-wing networks, if sued, would argue that Smartmatic and Dominion should be considered “public figures” — which would require the companies to prove that its critics were malicious or wildly reckless, not just wrong.

Mr. Connolly said he would argue that Smartmatic was not a public figure, a legal status whose exact meaning varies depending on whether Mr. Mugica files suit in Florida, New York or another state.

“They have a very good case,” another First Amendment lawyer who isn’t connected to the litigation, the University of Florida professor Clay Calvert, said of Smartmatic. “If these statements are false and we are taking them as factual statements, that’s why we have defamation law.”

Fox News and Fox Business, which have mentioned Dominion 792 times and Smartmatic 118 times between them, according to a search of the service TVEyes, appear to be taking the threat seriously. Over the weekend, they broadcast one of the strangest three-minute segments I’ve ever seen on television, with a disembodied and anonymous voice flatly asking a series of factual questions about Smartmatic of an expert on voting machines, Eddie Perez, who debunks a series of false claims. The segment, which appeared scripted to persuade a very literal-minded judge or jury that the network was being fair, aired over the weekend on the shows hosted by Lou Dobbs, Jeanine Pirro and Maria Bartiromo, where Mr. Giuliani and Ms. Powell had made their most outlandish claims.

Newsmax said in an emailed statement that the channel “has never made a claim of impropriety about Smartmatic, its ownership or software” and that the company was merely providing a “forum for public concerns and discussion.” An OAN spokeswoman didn’t respond to an inquiry.

I’m reluctant to cheer on a defamation case against news organizations, even networks that appear to be amplifying dangerous lies. Companies and politicians often exploit libel law to threaten and silence journalists, and at the very least subject them to expensive and draining litigation.

And defamation cases can also collide with subjects of genuine public interest, as in the most prominent case I’ve been involved in, when a businessman sued me and my colleagues at BuzzFeed News for publishing the Steele Dossier, while acknowledging that it was unverified. There, a judge ruled that the document was an official record that BuzzFeed was entitled to publish.

In this controversy, even the voting companies’ worst critics find the coverage wildly distorted.

“They’ve been mining every paper I’ve ever written and any deposition I’ve ever given and it’s nonsense,” said Douglas W. Jones, an associate professor of computer science at the University of Iowa who has long argued that voting software isn’t as secure as its vendors claim. He said Ms. Powell’s cybersecurity expert, Navid Keshavarz-Nia, called him on Nov. 15, apparently seeing him as a potential ally, and spent an hour going point-by-point over claims that would wind up in a deposition. “He seemed sane, but every time I would ask him for evidence that would support one of these allegations he would squirm off to a different allegation,” Mr. Jones said.

As the conversation wore on, he wondered, “Was someone trying to pull a ‘Borat’ on me?”

But the allegations are no joke for Smartmatic and Dominion. Mr. Mugica said he had taken worried calls from governments and politicians all over the world, concerned that Mr. Trump’s poison will seep into their politics and turn a Smartmatic contract into a liability.

“This potentially could destroy it all,” he said.

Mr. Mugica wouldn’t say whether he has made up his mind to sue. Mr. Connolly said that he has “a lot of people watching a lot of videos right now,” and that he’s researching whether to file in New York, Florida or elsewhere. I asked Mr. Mugica if he’d settle for an apology.

“Is the apology going to reverse the false belief of tens of millions of people who believe in these lies?” he asked. “Then I could be satisfied.”