CLEVELAND — Whether Sen. Ted Cruz’s speech here was standing up for principles or simply dissing RNC Chairman Reince Priebus to ready himself for 2020, the question now is whether Mr. Priebus will pursue his threat to enforce the pledge Mr. Cruz, Jeb Bush and John Kasich signed to support whoever is the Republican nominee.

In a July 5 recorded interview with The Washington Times Insights Club, Mr. Priebus said he regarded that pledge to be a “contract” that he intends to enforce.

Mr. Priebus said the signers had accepted “hundreds of millions of dollars worth of technology and data” assembled by the RNC, and in exchange, they “agreed to support the nominee.”

“This isn’t an optional thing,” Mr. Priebus said. “It’s a real slap in the face to the party not to honor your commitment to the party.”

Growing more heated in tone, Mr. Priebus told the holdouts: “Don’t run for the nomination signing the agreement then not honor it.” He suggested if that they don’t want to sign and honor agreements, they should “run for school board instead next time.”

Mr. Priebus did not respond to a query from The Washington Times on Thursday about whether he intends to enforce the support pledge that he has labeled as a “contract.”

But his chief strategist Sean Spicer texted this about his boss’ current view: “he believes a person is only as good as his word.”

Prominent Republicans were at odds over whether the pledge is enforceable as a legal contract but generally in agreement on the wisdom of trying to enforce it — or rather the folly of trying to.

“It would hurt the cause of party unity to try to hammer Ted Cruz, Jeb Bush and John Kasich to live up to their pledge,” said Texas GOP Chairman Tom Mechler.

Republican National Committee General Counsel John Ryder declined to comment on the record, but a senior party official said that rather than sue Mr. Cruz for breach of contract in order to try to force him to support Mr. Trump, the RNC could “cut off the flow of any data” he needs for a 2018 Senate re-election campaign and a 2020 run for the presidential nomination.

Speaking from the less politically sensitive position of RNC general counsel emeritus, David Norcross said “There’s no practical remedy at law to force Cruz, Bush and Kasich to endorse Trump because you have no tool to use.”

Whether relief for the anger so many Republicans feel toward Mr. Cruz is only a lawsuit away seems highly doubtful for several reasons.

“What do you get from suing Cruz, Kasich and Bush?” Mr. Norcross said. “There’s a big furor that turns the story into something bigger and it lasts longer.”

For many GOP leaders, the consequences should lie in the real nature of the pledge itself.

“If I were Reince, I would say to the holdouts, ‘You have taken the pledge and you have a moral obligation to support our nominee,’” said Mr. Norcross, who was in charge of the GOP’s highly successful 2004 national convention in New York City.

Hawaii delegate Willis Lee said legal and technical reasoning aside, by “attempting to make a federal case out of the pledge, you only create more disunity rather than help unify the party behind Trump.”

Top party lawyer James Bopp Jr. saw a constitutional road-closed sign in the middle of the litigious route.

“If the pledge is a contract and Cruz breached it, then Reince could have barred him from the debates,” said Mr. Bopp. “But the debates are over. So all that’s left is for the RNC to sue for specific performance of the agreement — for a court order requiring Cruz to endorse Trump.”

The problem with that, however, “is the First Amendment would prevent a court — that is, the government, which is what a court is in this context — from requiring a person to endorse a candidate if the person does not want to endorse,” Mr. Bopp said. “So there is no currently available remedy a court could order.”

More or less in line with her state party’s chairman, Texas delegate and Cruz supporter Diana Denman texted The Washington Times: “I think the RNC & all of us should move on! Too little time left before Nov.”

Across the GOP spectrum, the word seems to be a lawsuit wouldn’t be worth the filing papers they’d be written on.

“The one thing really important to people now is they want the rancor and division to stop,” said Heather Higgins, president of Independent Women’s Voice. “Anything that perpetuates that division is in their minds not what we ought to be doing, and suing [defeated candidates] to support Trump only perpetuates that division.”

As much as unity-seeking GOP leaders might like retribution for Mr. Cruz’s perceived self-serving actions Wednesday and Thursday, they shrink from the prospect of more intraparty warfare

“At this stage of the election cycle, I don’t support legal action to try to enforce the pledge,” Arizona GOP Chairman Robert Graham said. “We must stop fighting each other and stop the liberal agenda that is destroying our nation.”