Donald Trump’s delegates to the Republican nominating convention are proving to be exceptionally loyal, defying predictions by some analysts that they may flip their support to another candidate if Mr. Trump doesn’t win on the first ballot in Cleveland this summer.

Mr. Trump insists he will win on a first ballot, but his two remaining rivals, Sen. Ted Cruz of Texas and Ohio Gov. John Kasich, are banking on being able to deny him an outright majority. That would lead to a contested convention, where they try to stitch their own majority by winning over delegates no longer tied to Mr. Trump after the first ballot.

The outcome would then depend on the people serving as delegates — a process that has been completed in a handful of states. Interviews with The Washington Times show that those assigned to Mr. Trump say they are ready to stick with him at the Cleveland convention as long as he needs them.

“If Mr. Trump goes into the convention with the most delegates and someone else walks out of there and he is denied the first right of refusal, I will leave the Republican Party and I will work the rest of the my life to destroy it,” said New Hampshire state Rep. Daniel Tamburello, one of a slate of 11 Trump delegates from the Granite State. “If they deny him that and somebody else walks out of there against his will against the nominee, I will leave the party.”

Candidates earn a certain number of delegates with their performances in primaries and caucuses. The people selected to serve as delegates are generally bound to vote for the candidates to whom they are pledged — at least on the first ballot.

If nobody has the 1,237 delegates needed to win outright, many states release their delegates, who are then free to vote in later balloting for whomever they want. Since the people selected to serve as delegates are often longtime party loyalists, some Republican operatives hope those pledged to Mr. Trump can be swayed to switch after the first ballot.

Former Virginia Republican Party Chairman Jeff Frederick, who said he neither supports nor opposes Mr. Trump, said the anti-Trump forces should start working the delegates.

“I am going to call them, send them handwritten notes, mention their names at local events from the podium. I am going to make these people feel like rock stars,” Mr. Frederick said. “So if it does come to a second ballot, I have a pretty good shot of getting some of those people.”

Still, he said, it would be a heavy lift — particularly if Mr. Trump falls just short of winning the nomination outright.

“I think it is more wishful thinking,” Mr. Frederick said. “When delegates get to the convention knowing they represent millions of voters, I think there might be some pause.”

Indeed, Mr. Trump’s backers say he will not only keep his supporters, but he also will find a way to win over others.

“Donald Trump has stated repeatedly that he is the deal-maker,” said Duke Lowrie, an at-large Trump delegate from Louisiana. “Before a contested floor vote happens, the deal will be made. There are some who would love to anoint the nominee, like [2012 Republican nominee Mitt] Romney. But his and those like him have zero influence on me and how I will vote.

“Most all of the delegates are seasoned party politicos, who know the game and will not allow the party to be destroyed by a few power brokers. They are loyal to the party and will be the first to point out a problem in the process,” Mr. Lowrie said. “I do not see a movement of delegates one way or the other.”

Mr. Trump has captured 739 of the 1,237 needed to win the Republican nomination, according to the tally kept by The Associated Press. That puts him ahead of Mr. Kasich, who with 143 delegates is mathematically eliminated from winning the nomination on the first ballot, and Mr. Cruz, who with 465 delegates would need a miracle finish in the remaining primaries to claim a first-ballot win.

Mr. Trump, meanwhile, argues that he should tapped if he enters the mid-July convention with a strong plurality of voters.

Voters apparently agree.

A CNN/ORC poll released this week showed that 60 percent of Republicans and Republican-leaning independents said if no candidate has won a majority after the first round of voting at the convention, the delegates should vote for the candidate with the most support in the primaries and caucuses.

But Reince Priebus, chairman of the Republican National Committee, has made it clear that the rules allow delegates to nominate other candidates if Mr. Trump doesn’t earn a majority of delegates.

Asked whether he could envision himself switching camps, Richard Nordstrom, the mayor of Galva, Illinois, who was elected to serve as a Trump delegate, said, “I personally cannot.

“But we are not blood brothers by any means — I am not married to the guy,” Mr. Nordstrom added.

Other delegates pledged to Mr. Trump felt deeper ties. Mark Fratella, an eighth-grade teacher in Illinois, said he is “prepared to go all the way to the end for him.”

“Frankly, I think he is going to have the 1,237,” Mr. Fratella said. “However, if we are at a contested convention, I am willing to go two, three, four ballots for him, unless I am released by his campaign, but as far as I am concerned I am in until the bitter end.”

Stella Kozanecki, a delegate from Illinois, said she would stand by Mr. Trump throughout the process and would reject the Republican Party if she felt it resorted to dirty tricks at the convention.

“If that should happen, and there is a brokered convention and Donald Trump does not get the nomination, then I will not vote for any Republican for a very long time,” Ms. Kozanecki said.

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