Republican presidential candidate Donald Trump at the South Carolina Tea Party Convention in Myrtle Beach on Jan. 16. For the billionaire, the risks in skipping Thursday’s GOP debate are great — as are the potential rewards. (Timothy A. Clary/AFP/Getty Images)

On the eve of Fox News Channel’s Republican presidential debate here, there was no sign of a detente Wednesday between the network and Donald Trump, as the front-runner­ continued his boycott and some prominent conservative voices rushed to his defense.

After debate negotiations between Fox executives and the Trump campaign came to an abrupt end, Trump’s aides scrambled Wednesday to organize a “special event” Thursday night for him and his family at Drake University to benefit veterans organizations.

The event is scheduled to start at the same time as the debate and only a few miles from the Fox site. Campaign manager Corey Lewandowski said he has invited all other TV networks to broadcast it live, promising that Trump would be joined by “special guests.”

Trump appeared for an interview Wednesday night on Fox, where host Bill O’Reilly tried to persuade him to reconsider. But Trump, citing “the stupidity of Fox,” said that he was treated unfairly by the network and that walking away was the right call.

“When you’re mistreated, as we were with the Iran deal, our country should have walked,” Trump said. “I was not treated well by Fox. . . . I said, ‘How much of this do you take?’ ”

Sheriff Joe Arpaio, right, of Maricopa County, Ariz., endorses GOP candidate Donald Trump before a rally in Iowa, on Tuesday. Trump said he would not participate in the next Republican debate hosted by the Fox News Channel. (Scott Olson/Getty Images)

For Trump, the risks in skipping the debate are great — as are the potential rewards. With five days until the Iowa caucuses, Trump has been locked in an intense battle with Sen. Ted Cruz (Tex.) for the lead here.

Trump believes momentum has been on his side, and his strategy is to effectively run out the clock through Monday’s caucuses. By backing out of the debate, he avoids facing scrutiny from the Fox moderators — not to mention confrontations from his rivals — over his past positions on social issues, which have been the subject of negative TV advertisements in Iowa.

Trump hopes he shows strength by standing up to a network — and anchor and co-moderator Megyn Kelly — he does not consider impartial.

But Trump’s gambit creates an opportunity for Cruz and other opponents to strike blows on Trump in front of a national TV audience without him being there to counterpunch.

Trump also risks seeming peevish and weak. As some of his rivals said, if he shrinks from Kelly’s questions, how could Trump stand up to an adversary such as Russian President Vladi­mir Putin?

“Poor little Donald, being mistreated,” Jeb Bush said mockingly Wednesday. The former Florida governor wagered $20 that Trump would show up at the debate.

Strategist Stuart Stevens, who guided GOP nominee Mitt Romney’s 2012 campaign, said that “American voters don’t tend to respond well to people who think that they’re above the process. What Trump is saying is: ‘I’m better than everybody else. I don’t need to do this.’ ”

Republican Donald Trump is saying he "most likely" won't attend the debate Fox News anchor Megyn Kelly is set to co-moderate. Here's a look back at the clash that started with an earlier debate in August 2015. (Sarah Parnass/The Washington Post)

The reaction among various conservatives, however, was different. Radio host Rush Limbaugh, who has not always seen eye to eye with Trump, said this was the latest masterstroke by the unconventional politician.

“Donald Trump knows that by not showing up, he’s owning the entire event,” Limbaugh told his listeners Wednesday. “Some guy not even present will end up owning the entire event, and the proof of that is Fox News last night.”

Limbaugh added: “Trump is so far outside the formula that has been established for American politics that people who are inside the formula can’t comprehend it.”

Longtime Trump associates said the mogul’s tactics are similar to the ones he used when he was ubiquitous in New York City’s tabloids and a reality-TV star.

Several of them pointed to Trump’s best-selling business book “Trump: The Art of the Deal” as a guide. One Trump friend, requesting anonymity to speak candidly, said that “Page 98 tells you everything.” In that part of the book, Trump has a conversation with his onetime political mentor, the combative and controversial lawyer Roy Cohn: “I’d rather fight than fold, because as soon as you fold once, you get the reputation of being a folder,” Trump said.

Trump’s tightknit inner circle, which has been camped out in Iowa since Sunday, had been preparing for the debate for weeks in its usual fashion. The policy team, led by Iowan Sam Clovis, compiled briefing books. Lewandowski touched base with friends on Capitol Hill, where he once worked.

Trump’s boycott was met with internal agreement, people familiar with the campaign said. Lewandowski and spokeswoman Hope Hicks, who shared Trump’s frustrations with Fox since the August debate, did not question their boss’s decision and moved to arrange the alternative event for Thursday.

Lewandowski said the final straw for Trump was Fox’s Tuesday news release — he called it a “missive” — mocking and belittling the candidate, suggesting he would seek advice from his Twitter followers if the “Ayatollah and Putin” treated him unfairly.

“This is not about Megyn Kelly,” Lewandowski said. “This is about a network that is not treating Mr. Trump fairly.”

The unusual Fox statement seemed to give Trump cover to back out of the debate.

“I do think the statement crossed the line because it went into questioning whether or not the candidate was fit to be president,” said Brett O’Donnell, a Republican debate coach.

When multiple GOP officials called Wednesday to privately inquire about whether Trump was pulling a stunt and would appear on the debate stage after all, Lewandowski insisted that Trump meant what he said and would not appear.

The Republican National Committee tried to navigate the situation carefully, looking to sustain its relatively warm relationships with both Fox News and the Trump campaign. Sean Spicer, the RNC’s chief strategist, was on the phone regularly with Lewandowski on Wednesday, not to urge him to reconsider but to get status updates, several Republicans said.

Some veteran political strategists saw little upside for Trump.

“I’m very surprised by this,” said Ed Rollins, who has worked on many past GOP presidential campaigns. “He’s done well in the debates. He’s a performer. . . . He’ll be a part of the debate whether he’s on stage or not, but he won’t be there to defend himself. It’s just not a smart move. You look small and petty.”

Newt Gingrich, the former House speaker and 2012 Republican presidential candidate, said Trump was making “a substantial mistake, creating a vacuum and a new dynamic where someone could emerge.”

“No one should be confident that this thing is locked down, and voters can change with amazing speed,” Gingrich said.

Cruz is hoping to take advantage of that vacuum.

He suggested that Trump was afraid to face questions about his record and challenged him to a “mano-a-mano”­ debate before the Iowa caucuses.

“Certainly, Ted Cruz, who is a good debater and also a master of theatrics, will definitely take the opportunity, even if there’s not an empty podium, to pretend like there is one,” O’Donnell said. “He’ll be fighting Trump the entire night.”

Trump’s absence frees up airtime for Cruz and other candidates, such as Sen. Marco Rubio (Fla.), to debate one another and make their closing arguments to Iowa voters. Rubio sought to distance himself from what he called the “sideshow” of Trump and Cruz, offering himself as a more serious leader who is capable of healing the Republican Party’s divisions.

“These kinds of theatrics by Ted Cruz and Donald Trump are an entertaining sideshow, but they have nothing to do with defeating Hillary Clinton,” Rubio said in a statement, referring to the Democratic presidential candidate. “We don’t have time for these kinds of distractions.”

It remains to be seen how extensively the other candidates will be able to attack Trump on stage or whether the Fox moderators will attempt to steer the conversation away from the absent billionaire.

“Everyone will try to turn this into a moment to show a little leg and convince the voters of Iowa that Trump has ridiculed them before and now this is one more insult,” said GOP consultant Rick Wilson.

Asked to assess how the debate boycott may affect Trump’s candidacy, Fred Davis, a Hollywood-based Republican image guru who produces ads for Ohio Gov. John Kasich’s super PAC, summed up the political world’s befuddlement.

“Conventional wisdom says the ‘wimp factor’ would hurt him,” Davis said. “But since when has conventional wisdom applied to Mr. Trump?”

Costa reported from Washington and Johnson from Iowa City. Ed O’Keefe in Des Moines contributed to this report.