While Donald Trump turns his campaign attacks toward his own party -- alleging the nominating process is “rigged” -- he's missing critical deadlines and being outmaneuvered by the Ted Cruz campaign, as frustrated party leaders tell the front-runner: "Give us all a break."

The billionaire businessman said Tuesday night at a CNN town hall that he knows the rules “very well” but those rules are “stacked” against him by the establishment.

That prompted a cutting retort from Republican National Committee Chairman Reince Priebus.

The dispute over process is building as Cruz’s operation has proved more adroit lately in getting supporters elected as the actual delegates who will attend July’s convention. Last weekend at the Colorado state convention, he gained all 34 delegates to this summer's convention in Cleveland.

On the sidelines, he’s also working to get allies elected as delegates in states that – unlike Colorado – hold traditional primaries and caucuses that allocate delegates based on voting.

In those states, delegates “bound” to Trump or Cruz or Ohio Gov. John Kasich would have to vote for their respective candidates on the first ballot at the convention. But if there’s an open convention – meaning nobody has the necessary 1,237 delegate to clinch the nomination – Cruz is banking on his delegate allies to surge over to his side on a second ballot, which many would be allowed to do.

The Washington Post reported Wednesday that based on their own analysis, Cruz could pick up at least 130 – and as many as 170 or more – additional delegate votes on the second ballot at an open convention.

This would make it even harder for Trump to lock down the nomination, upping the pressure on the front-runner to clinch the party nod by the final June contests. The campaign has insisted they can do this, and that Cruz won’t get the opportunity to use his backup delegate allies on a second ballot.

But the Trump campaign has made it harder on itself by missing crucial deadlines in a number of states to lock up delegates who would stay loyal beyond the first ballot.

Trump's team is only now starting to engage in the delegate selection process, the choosing of the actual people who will attend and vote at the convention. Republicans have already selected delegates in at least nine states. And in others, such as Virginia and Arizona, the deadline to apply to be a delegate has passed.

Indiana's primary, for example, won't take place until next month. But the deadline to become a national convention delegate was in mid-March. Anti-Trump forces reportedly have already been lining up delegates who would turn on Trump at a contested convention.

"Are we concerned? Yes, definitely," said Tony Samuel, vice chairman of Trump's Indiana campaign.

The Cruz team feels the opposite.

"Even if (Trump) jumped into high gear, he can't do it," said Shak Hill, a Cruz campaign leader in Virginia. "That's where he's been shut out of the game."

Trump is just ramping up his operation, but in some states he's too late.

In Virginia — a state where Trump won the primary — he has missed the deadlines to assemble lists of potential delegates. Cruz, however, has delegate candidates in 10 of Virginia's 11 congressional districts.

The application deadline was last month.

Indiana's primary is May 3, but 27 of the state's 57 delegates — the actual people — have already been selected at congressional district caucuses. The deadline to register as a candidate for delegate was March 15.

In the at least nine states that have picked some or all of their delegates, Trump has won a total of 100 delegates in primaries and caucuses in these states. In most, however, the candidates had no formal role in selecting the people who will fill those slots.

Trump, meanwhile, is banking on rallying popular support – which so far has kept him far out in front in the Republican field – in hopes of winning the nomination outright.

"Our Republican system is absolutely rigged. It's a phony deal," Trump told a rally in a packed airport hangar in Rome, N.Y., Tuesday evening.

"These are dirty tricksters," he said, placing the blame on the Republican National Committee. "They should be ashamed of themselves for allowing this kind of crap to happen," he added.

He went further a few hours later during the CNN town hall in New York City, suggesting the RNC was actively working to defeat him.

"The RNC doesn't like this happening. They don't like that I'm putting up my own money because it means they don't have any control over me," Trump said.

Cruz tore into Trump in a radio interview Tuesday, accusing his rival of being a bully, inciting violence and using dirty tricks to intimidate voters and delegates. Cruz unloaded on Trump over reports that his supporters were publishing the home addresses of delegates in Colorado and threatening to make public the hotel room numbers of delegates at the convention this summer.

"That is the tactic of union thugs," Cruz told host Glenn Beck. "That is violence. It is oppressive."

Cruz conceded that Trump will do well in upcoming primaries, including in Trump's home state of New York next Tuesday. Cruz said he will fare better when the race shifts back west to Indiana, Nebraska, South Dakota and Montana, before finishing in California on June 7.

The Associated Press contributed to this report.