The video, from the YouTube channel "Real Americans 4 Real Presidents," which is not affiliated with the Trump campaign, highlights an apparent contrast between Cruz's support for the policy in 2011 -- when he said it was a "mistake" to try to fight birthright citizenship -- and comments he made in 2015, insisting he has opposed it "for many years."
In the 2011 footage, from an interview with Texas radio host Duke Machado at a candidate forum while he was running for a U.S. Senate seat, Cruz insists, "The 14th Amendment provides for birthright citizenship. I've looked at the legal arguments against it, and I will tell you as a Supreme Court litigator, those arguments aren't very good."
Cruz adds, "As much as someone may dislike the policy of birthright citizenship, it's in the U.S. Constitution."
(The 14th Amendment states that "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and the state wherein they reside.")
The new video then cuts to Cruz discussing birthright citizenship in 2015, after Trump brought the issue into the spotlight of the presidential race by announcing his opposition to it.
"So (Trump) recently came out against birthright citizenship. I've had that position for many years, back in 2011 when I was running for the U.S. Senate," Cruz said. "I said very explicitly then, we should end birthright citizenship, and I still think that's the right position."
The video then ends with a coin flipping in the air and the caption "Which Cruz will you choose?"
Cruz communications director Rick Tyler appeared on "New Day"
on CNN Tuesday morning and sharply criticized Trump, saying he "just wants to lash out and call names. I don't find that very presidential."
The Trump team's attack comes as hostility between its camp and the Cruz campaign is at an all-time high. The GOP rivals are locked in a close race in Iowa while national polls
show Cruz gaining ground.
Tyler also pushed back on Trump's recent criticism that Cruz is a "nasty guy" and disliked by his colleagues in Congress.
"Washington doesn't like Ted Cruz," Tyler contended. "Newsflash, Donald Trump: they don't like him. You know why they don't like him? Because he's the guy who'll go in there and shake it up."
He continued, "Donald Trump wouldn't go and shake it up. He would go in there and make deals. He would compromise. He's been the paymaster for the cartel for a long time."
And on Monday night, Cruz added fuel to the fire when he slammed Trump in an interview with NPR
, charging that Trump's temperament made him poorly suited to the presidency.
"I think the American people want a steady hand at the helm," Cruz argued. "They want someone they know and trust."
"They don't want to wake up every day wondering if the latest polls might set off the commander in chief into a frenzy of tweets."
With the first votes in the 2016 election set to be cast in less than two weeks at the Iowa caucuses, the race doesn't seem likely to cool off anytime soon.