"I was there and I saw the debate and I saw Ted Cruz say we'll take citizenship off the table and then the bill will pass and I'm for the bill, the bill will involve legalization," Paul said. "He can't have it both ways."

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"What is particularly insulting, though, is that he is the king of saying, 'Oh you're for amnesty. Everybody is for amnesty except for Ted Cruz,'" the White House hopeful continued. "But it's a falseness."

"And that's an authenticity problem — everybody that he knows is not as perfect as him because we're all for amnesty," Paul said, mockingly, before adding, "I was for legalization. I think frankly, if you have border security we can have legalization. So was Ted, but now he says it wasn't so. That isn't true."

Cruz retorted that he "led the fight against amnesty" with hard-line conservative lawmakers such as Sen. Jeff Sessions (R-Ala.) and Rep. Steve King (R-Iowa). He said he fought against the 2013 bipartisan bill supported by rival Marco Rubio by offering an amendment to strip out a path to citizenship.

Still, Cruz faced faced a barrage of criticism from Rubio in the debate, with the Florida senator saying Cruz's campaign was based on a "lie" of him being the most conservative on immigration, accusing Cruz of flip-flipping on the issue, saying, "now, you want to trump Trump on immigration."

Cruz and Donald Trump, who did not participate in the debate, are favorites in the Republican Iowa caucuses on Monday.