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Cruz, the senator from Texas, mentioned Democrats like Sen. Chuck Schumer of New York, whom he said Trump has "written checks to repeatedly."
Cruz used that to argue that Trump couldn't be trusted to appoint a Supreme Court justice to replace the late Antonin Scalia. He said any Supreme Court justice appointed by Trump would "be a left-wing judicial activist who will undermine religious liberty."
Trump shot back, saying that Cruz was "the primary supporter of John Roberts," the high court's current chief justice, who was appointed by President George W. Bush. Cruz has since criticized him over the Supreme Court's rulings to uphold key provisions of President Barack Obama's Affordable Care Act, colloquially known as Obamacare.
In a 2005 column, Cruz wrote of Roberts: "As an individual, John Roberts is undoubtedly a principled conservative," noting that his "approach will be that of his entire career: carefully, faithfully applying the Constitution and legal precedent."
Cruz said Trump's statement about his support of Roberts was "flat-out false."
"Donald has a tenuous relationship with the truth," Cruz said. "I wrote one op-ed supporting President Bush's nomination after he made it. I would not have made that nomination."
As Cruz continued talking, Trump cut in and said, "That is not what you said in the op-ed."
Cruz responded by taking an apparent shot at Trump's temper.
"Donald, please, I know it's hard not to interrupt, but try," he said.
Trump continued repeating his attack.
"Breathe, breathe, breathe," Cruz said. "You can do it. You can breathe. I know it's hard."
Rubio jumped into the fray.
"When they're done with the yoga, can I answer a question?" Rubio said.
"You cannot," Cruz joked back. "I really hope that we don't see yoga on this stage."
"Well, he's very flexible, so you never know," Rubio retorted, referring to Trump, who had said earlier in the debate that successful people need "a certain degree of flexibility."