Specifically, The Donald campaign has been attacking Cruz's Oval Office eligibility on the grounds that he was born in Calgary, Canada, and not the United States.
Meanwhile, other Republican presidential campaigns have smaller footprints.
Next Monday, Iowa residents will gather in schools, churches and even private homes to choose among the Republican and Democratic candidates battling to be their party's 2016 presidential nominee " the first in a series of state-by-state contests to choose delegates to each party's presidential nominating convention.
A spokeswoman for the Trump campaign did not return a request for comment on those accusations. Cruz is believed to have assembled a strong get-out-the-vote operation.
In Iowa, Plymouth County GOP Chairman Don Kass called it "typical Trump" and said the candidate could benefit by "making a bigger splash" with his own event.
Republicans, more than Democrats, think Trump is religious. But the fireworks Tuesday were on the Republican side.
The statement says Mr Trump will instead host an event in Iowa to raise money for "the Veterans and Wounded Warriors".
According to a Wednesday Monmouth University survey, a victory for Trump in the Iowa caucus hinges on whether his non-traditional campaign style motivates irregular voters to caucus for him. Trump was outraged, and later said on CNN that Kelly had "blood coming out of her eyes, blood coming out of her wherever" with her angry questioning. She said her network and CEO Roger Ailes had made it clear to Trump for months that they wouldn't change their moderator line-up.
"I'm old school", Kamlet said.
Cruz could also go after Trump, who has close ties to Wall Street interests, for supporting the financial bailout of 2008.
Debates have always been considered critical moments for voters and candidates alike, and Fox News was more pointed than the RNC in its response to Trump's decision to sit their event out. But the situation has persisted, along with concerns that the Trump campaign may be using the Secret Service to enforce its restrictions on the media.
"In a call on Saturday with a FOX News executive, Lewandowski stated that Megyn had a "rough couple of days after that last debate" and he 'would hate to have her go through that again.' Lewandowski was warned not to level any more threats, but he continued to do so". The real estate mogul had threatened repeatedly to boycott debates before, only to ultimately acquiesce. Ted Cruz, R-Texas, for president and began volunteering for his campaign.
There were plenty of reasons Donald Trump's last-minute withdrawal from the Republican debate could be a bad move, BBC North America reporter Anthony Zurcher said.
"If someone did that, didn't show up at the interview, you know what you'd say?" University of Iowa police confirmed in a statement to NBC News that the man, 28-year-old Andrew Joseph Alemano, threw the tomatoes but did not hit the candidate.
The long-discussed meeting between the sitting president and his sometime critic is a moment for the president to display public neutrality in the heated and unexpectedly tight primary race to replace him - refuting suggestions that he's in the can for Clinton.
About 48 percent of adults think Hillary Clinton is a religious person. So far, only former Maryland Gov. Martin O'Malley, who is polling in the low singled digits, has said he'll participate.
China data brings relief, oil rebounds
Carmaker Ford (F) set a special dividend worth $1 billion, but its outlook for the year failed to impress analysts on Wall Street. This contrasted with market expectations where a further retrenchment of 4.1% had been predicted.
