Trump keeps heat on Cruz following debate

Donald TrumpDonald Trump GOP lawmakers give Trump bad reviews on debate performance Overnight Cybersecurity: FBI probes possible hack of Dems' phones | Trump's '400-pound hacker' | Pressure builds on Yahoo | Poll trolls run wild Trump on debate: I was 'holding back' MORE is keeping the focus on presidential rival Ted CruzTed CruzFunding bill rejected as shutdown nears Cruz: Clinton 'tired' and 'formulaic' during debate The Trail 2016: Fight night MORE a day after they sparred heavily in a GOP debate, slamming the Texas senator on Friday for having "lied" about his poll numbers and Canadian birth.

"I don't know about being a nice guy, I'm not sure," Trump said of Cruz from Iowa on MSNBC's "Morning Joe," which opened with a handful of Trump protesters being escorted out.

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"I think he had a couple of suits filed yesterday against him running," said Trump, who has repeatedly argued that Democrats will sue Cruz over his eligibility for the presidency.

A Houston attorney has filed a lawsuit saying Cruz should be disqualified from the race because he isn't a "natural-born citizen" under the Constitution, Bloomberg reported.

A raucous moment erupted in Thursday night's debate in South Carolina when Cruz and Trump battled over the senator's Canadian birth, with Cruz bringing up Trump's Scottish mother.

Cruz has argued that he is eligible for president because he was born to an American mother, saying Thursday night that he wouldn't be taking legal advice from his outspoken rival.

The self-described "bromance" between the pair has officially fizzled, with Trump continuing to bash Cruz on Friday, ripping his "disgraceful" knock on "New York values."

Trump also blasted the idea of being Cruz's vice presidential pick, saying Cruz "hasn't done well in the polls" and "really lied" about how well he's doing against the billionaire businessman.

"For him to lie about the polls ... I don't even want to think about that," Trump said.

"He's a good debater, but he's very strident. A lot of people aren't going to like that."