National GOP front-runner Donald Trump and Iowa favorite Ted Cruz clashed over issues as ephemeral as "New York values" and as practical as Cruz's Canadian birth, as they each sought to gain an advantage in the Jan. 14 Republican presidential debate hosted by the Fox Business Channel.

"I guess the bromance is over," Trump later summarized the encounter, CNN noted, in an allusion to the once-friendly relationship between the real estate tycoon and the Texas senator.

Early on in the debate, held in North Charleston, South Carolina, Fox Business host Neil Cavuto turned to the issue of Cruz's presidential eligibility, on which Trump had repeatedly cast doubts in recent weeks because the senator was born to an American mother in Calgary, Canada.

Cruz: Iowa polls behind citizenship argument

"Donald Trump and others have said that being born in Canada means you are not natural-born," Cavuto summarized. "Do you want to try to close this topic once and for all tonight?"

The "birther" argument was a non-issue, Cruz replied, adding that Trump's motivations were obvious.

"I recognize that Donald is dismayed that his poll numbers are falling in Iowa," he said. "But ... under longstanding U.S. law, the child of a U.S. citizen born abroad is a natural-born citizen."

But Trump repeated his argument that Democrats would eventually challenge Cruz's eligibility in court.

"You have a big lawsuit over your head while you're running," Trump told his rival. "And if you become the nominee, who the hell knows if you can even serve in office?"

Trump: "New York values" term is offensive

Moments later, the former "Apprentice" star said he was offended by comments Cruz had made earlier this week, suggesting that Trump "embodies New York values." Cruz doubled down on the comment in the debate by saying, "Most people know exactly what New York values [are]."

"When the World Trade Center came down (on Sept. 11, 2001), I saw something that no place on Earth could have handled more beautifully, more humanely than New York," Trump countered. And, naming National Review founder William F. Buckley, the front-runner added that "(some) conservatives actually do come out of Manhattan."