The immigration debate within the crowded field of 2016 GOP White House hopefuls -- long focused on Donald Trump and his controversial comments about Mexican migrants -- has now turned to Cuban-American Sens. Ted Cruz and Marco Rubio, who have been battling over just how different their views on the issue really are.

Cruz has begun to go hard after his Republican rival over Rubio's support of a 2013 proposal for comprehensive immigration reform and told conservative radio host Laura Ingraham that the Florida senator was not fooling anybody with tougher rhetoric he has employed in recent months, Time reported.

"Talk is cheap," the Texas senator contended. "You know where someone is based on their actions."

Rubio, for his part, accused Cruz of flip-flopping on the issue, suggesting his colleague had backed the legislation before he opposed it, CNN noted.

"When the Senate bill was proposed, [Cruz] proposed legalizing people that were here illegally. He proposed giving them work permits," Rubio said. "He's also supported a massive expansion of the green cards. He's supported a massive expansion of the H-1B program -- a 500 percent increase. So, if you look at it, I don't think our positions are dramatically different."

The feud between the two presidential candidates, meanwhile, is raising eyebrows among GOP operatives who fear that the debate could turn into a race to the right on immigration, an issue that already makes their part vulnerable with Latino and Asian-American voters in the general election, Bloomberg explained.

Katie Packer Gage, the deputy campaign manager for 2012 Republican presidential nominee Mitt Romney, told the publication that alienating Latinos continues to be a poor strategy.

"I have a huge concern," she said. "If you look at where Donald Trump is with Hispanic voters, he literally is in the sewer. For now I don't think Hispanic voters necessarily equate that with the party."

But "candidates like Ted Cruz trying to drive our party further to the right" on the immigration issue could well turn out to be a "problem" for Republicans, Gage concluded.