With Donald Trump’s overwhelming victory in New York killing off Ted Cruz’s chances of being able to attain a 1,237 majority of delegates before July’s GOP convention, the Texas senator is casting his hopes on a contested convention – where most delegates will be “unbound” by the second ballot and able to vote as they choose.

But there are risks to that strategy.

Even if Cruz is able to force a contested convention by keeping Trump from reaching the magic 1,237 number, he is counting on delegates both having the strength to vote to reject Trump in the face of significant pressure from the campaign and Trump supporters, and then moving to Cruz after they are unbound.

While the strategy seems to have its merits, the question of whether delegates will back him could be complicated by recent threats made to both GOP party officials and delegates themselves, allegedly by Trump supporters.

Colorado GOP Chairman Steve House received death threats after the state’s convention, in which Cruz locked up the support of most of the delegates. House said that he received thousands of angry calls from Trump supporters, with some threatening his family, angry about the way the delegates are selected. He has referred the matter to the police.

Earlier this month, Trump adviser Dan Scavino posted the Tennessee GOP Chairman Ryan Haynes’ cell phone number on Twitter, telling supporters to “Let him know you support the TRUMP delegates!” and accusing Haynes of wanting “to STEAL your vote TODAY.”

Haynes told Politico he nearly canceled the delegate selection meeting after receiving a firestorm of abuse and threats.

But the threats have extended beyond just GOP officials. Politico reported Thursday that Craig Dunn, an Indiana delegate who criticized Trump, received a note warning “traditional burial is polluting the planet” that said ominously “we are watching you.”

Dunn, a Kasich supporter, told the outlet he’s most nervous about exiting the convention arena in the moments after a potential Trump loss.

“That’s where there’s the greatest prospect for danger,” he said. “I don’t see myself walking outside the convention with a Kasich badge.”

Dunn was one of at least four Indiana delegates who received disturbing messages — some of which have been investigated by police, Politico reported.

The billionaire frontrunner has done little to dissuade supporters from making such threats. In March he said “I think you’d have riots” if the party attempted to block his nomination.

The threats raise the question of whether delegates – many of whom have little-to-no experience of the white hot intensity of national politics – may feel unable to vote their conscience.

Officials in Cleveland say that they are working hard to secure a safe convention and planning is “well underway." RNC spokeswoman Alee Lockman told FoxNews.com the Secret Service is taking the lead.

“The Cleveland Department, Cuyahoga County Sheriff, the FBI and other security agencies are working closely with the Secret Service relative to developing the security plan for the Convention,” Lockman said. “There are Secret Service agents on the ground in Cleveland and they are making good progress.”

Local branches of the GOP expressed their confidence that delegates will not be harassed. Kyle Kohli, a spokesman for the Colorado GOP, told FoxNews.com that there had been a recent call with convention staff on the very issue of security for delegates.

“The security is so good in Cleveland that there’s not going to be a notion of threatening appearances at hotel rooms, as Secret Service and convention staff are going to be so well organized,” Kohli said.

The city of Cleveland is also making preparations, spending over $800,000 on riot-control suits and batons for police working during the convention amid fears of rioting and violence, Cleveland.com reported.

Kohli said there was little officials could do about threats to delegates on social media.

“That’s going to be there one way or another. It’s not something we’re overly concerned about, we think our delegates will be secure and will exercise good judgment and not be influenced by either stuff online or people showing up,” Kohli said.

Taylor Mason, spokesman for the Iowa GOP, echoed Kohli’s sentiments and said they weren’t too worried about delegates being swayed.

“People in Iowa are not really easily scared,” Mason said. “[Threats] wouldn’t be a deterrent.”

A spokeswoman for the Pennsylvania GOP also told FoxNews.com they have no concerns about the convention.

The Cruz and Trump campaigns did not respond to requests for comment from FoxNews.com. But in March, the Trump campaign told FoxNews.com they are in the process of trying to woo as many unbound delegates as possible ahead of the convention.

“The unbound ones we’re going after pretty strongly,” Barry Bennett, a senior adviser to the Trump campaign, said. “We aren’t going to waste resources on them, but if you’re 'wooable' we plan to woo.”

Bennett also raised the possibility that delegates who are lined up behind Cruz could fall to the wayside once the convention starts, at which point his support will evaporate as they line up behind a more moderate candidate such as Ohio Gov. John Kasich.

"This is where I think Cruz is being taken for a ride," Bennett said. "The establishment is using him because they want to get to the second ballot, and then they'll pretend they've never heard of him."

Kasich could also cause problems among some unbound delegates for Cruz. In Pennsylvania, where a primary is held Tuesday, delegates are not bound to any candidate either, but Cruz’s campaign has been working hard behind the scenes to get his people in place.

However, there is some high-level support for Kasich in the Pennsylvania GOP — including former Gov. Tom Ridge and national GOP committeeman Bob Asher — and that creates the potential that a bloc of delegate votes will favor Kasich.

The Associated Press contributed to this report.

Adam Shaw is a Politics Reporter and occasional Opinion writer for FoxNews.com. He can be reached here or on Twitter: @AdamShawNY.