CLEVELAND — Ted Cruz rolled the dice on his political future Wednesday night by refusing to endorse Donald Trump, firmly planting himself in a camp with other establishment GOP holdouts and setting himself up for a 2020 run at the White House — but the early betting is that his risk won’t pay off.

The morning after he was jeered off the stage, Mr. Cruz defended his decision, telling the Texas delegation to the convention Thursday that his beef with Mr. Trump is personal, not political. He said the billionaire businessman had bullied his wife and father during the campaign.

Strategists said Mr. Cruz appears to be counting on a Trump loss this year, and the Texas senator hopes he’ll be the early front-runner in four years. Delegates, though, said there’s fat chance of that happening after this week.

“Cruz is finished,” said New York delegate Sal Calise, who said the Texas senator had been his second choice in the presidential primary behind Ohio Gov. John Kasich. “His speech was pathetic, absolutely pathetic. I will never, ever, support him.”

On Wednesday Mr. Cruz mentioned Mr. Trump just once in his speech, congratulating the victor on his win. Mr. Cruz then urged voters to vote their “conscience” — a word that, during the GOP convention, has been code for snubbing Mr. Trump.

Within hours of his speech, Mr. Cruz was fundraising off it, vowing that his own political movement will continue. He still has two years left before he needs to seek re-election to the Senate.

Speaking to the Texas delegation Thursday morning, Mr. Cruz said he’d already told Mr. Trump earlier in the week no endorsement would be coming. He said he deserves credit for showing up when other presidential candidates who’ve refused to back Mr. Trump stayed home from the convention.

And he also challenged the notion that his remarks were detrimental.

“In that speech last night, I did not say a single negative word about Donald Trump,” he said. “And I’ll tell you this morning and going forward, I don’t intend to say negative things about Donald Trump.”

Still, he did little to tamp down the notion that he’s laying the groundwork for a 2020 bid. Indeed, earlier Wednesday, he basked in the chants of “2020” from supporters at a rally outside the convention site.

Ex-Arkansas Gov. Mike Huckabee, a two-time presidential hopeful, said Mr. Cruz damaged his brand.

“I think he did far more damage to himself than the party,” Mr. Huckabee told The Washington Times. “I thought here was a guy who started out with a great speech, could have landed and had a wonderful accolade, and instead crashed it right in the middle of the airshow.”

Mr. Huckabee said some of Mr. Cruz’s strongest supporters have since said the Texan committed political suicide. “They are embarrassed by him,” Mr. Huckabee said.

J. Todd Inman, a delegate from Kentucky, said four years is a long time in politics, and Mr. Cruz could work to rehabilitate himself, but some hard-core GOP activists won’t ever forgive him for the snub. “You don’t sass a man in his own house,” he said.

Mr. Cruz isn’t the only Republican candidate to refuse to endorse Mr. Trump. Mr. Kasich and former Florida Gov. Jeb Bush have been outspoken in saying they cannot vote for him and are publicly pondering their alternatives.

But Mr. Cruz is the only one who showed at the convention — and accepted a prime speaking slot.

As badly as Mr. Cruz may have played within the arena though, those watching at home were more forgiving. Drew Margolin, a Cornell University professor who tracks Twitter reactions, said the Texas senator didn’t burn bridges with the broad spectrum of Republican voters who have been reluctant to back Mr. Trump.

“My gut sense is that Cruz enabled them to express their true feelings,” Mr. Margolin said. “The convention crowd may have booed Cruz, but the Republicans at home that Trump is reaching out to were cheering, according to our data.”

Michael McKenna, a GOP strategist, said those people could be the opening Mr. Cruz needs.

“Cruz was speaking to the 70 percent of the nation that has serious reservations about Trump. He positioned himself as the leader of the anti-Trump” Republicans, Mr. McKenna said. “That’s going to be a good place to be, even if [Trump] wins. He did what most of the elected officials in the party want to do but don’t have the nerve.”

Going in Mr. Cruz’s favor is that the GOP has traditionally loved “repeat” candidates. The party’s nominee in 1968, 1972, 1980, 1984, 1988, 1992, 1996, 2004, 2008 and 2012 — every election but two in the modern primary system — was someone who already had run for president in a previous cycle.

The only modern exceptions are President Gerald Ford, who assumed office only after the resignation of President Richard Nixon; President George W. Bush, whose father had been president; and now Mr. Trump.

Mr. Cruz appears to be explicitly crafting his strategy after that of President Reagan, who lost the nomination to Ford in 1976 but won it four years later. Mr. Cruz’s speech Wednesday even adopted the same rhetorical conceit in his speech, saying the future will judge the results of this election.

Craig Shirley, a Reagan biographer, said Mr. Cruz delivered “a hell of a speech and one that could have served as his own acceptance remarks.

“But it also elicited strong reactions in the hall, both supportive and in opposition. Reagan’s, on the other hand, were pretty uniformly praised,” he said. “One thing is for sure. The GOP is just as divided today as it was in 1976.”

After Reagan’s speech, there was a sense among some Republicans that they’d nominated the wrong man.

“I am not sure Cruz elicited that same response tonight, but had Ford won in the fall, Reagan’s speech would probably have melted into the ether of history,” Mr. Shirley said. “So it remains to be seen if Trump wins or loses to see if Cruz’s speech becomes a launch pad or landing pad.”

• Seth McLaughlin contributed to this article.

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