TRUSSVILLE, Ala. — Ted Cruz woke up Sunday morning to a fresh barrage of charges of inconsistency from his Republican rivals for the White House, allegations that go far beyond his battle with Marco Rubio over their roles in the 2013 immigration debate.

In TV interviews, at least three of his GOP opponents raised accusations new and old that the Texas senator is anything but the "consistent conservative" he claims to be on the campaign trail. Joining Rubio in the Sunday morning pile-on were U.S. Sen. Rand Paul of Kentucky and former Florida Gov. Jeb Bush.

Leading the charge has been Rubio, the Florida senator who has been tangling with Cruz for weeks over a range of issues — most sharply immigration. Rubio has charged Cruz with being unclear on how he would deal with the 12 million people already in the country illegally, while Cruz has countered that he has never wavered in his oppostion to providing any form of "amnesty" to them.

"There are multiple issues in which he has tried to do these sort of things," Rubio said on CBS's "Face the Nation." "If you're going to attack someone on a policy issue, you need to be clear where you stand on the issue, and where you stood in the past." 

While Rubio renewed his claims against Cruz on immigration and foreign policy, the Floridian received some help on another show from Paul. 

"I think on a number of issues, he wants to have it both ways, depending on which audience he's talking to," Paul said on CNN's "State of the Union," adding that Cruz was being especially deceptive on immigration. "I think he should just admit that he changed his mind — that he used to be for legalization but he's not anymore."

As Paul spoke, his campaign released a Web video that offered up four issues on which Cruz has allegedly flip-flopped: how to deal with people in the country illegally; whether the United States should accept Syrian refugees; Trade Promotion Authority, a measure that gave President Barack Obama power to fast-track trade agreements and the reauthorization of the Patriot Act. After each charge, the video replays a clip of Cruz stuttering during an interview last week on Fox News in which he was pressed about his immigration position. 

Paul did not let up on Cruz in a fundraising email sent to his supporters hours later, writing that Cruz was "all for allowing illegal immigrants to stay in 2013, but now he is vying for the bus driver position on Donald Trump's deportation express." In recent days, Cruz's campaign has been emphatic that his priority is "attrition through enforcement," or deporting those in the United States illegally first and foremost.

Cruz also took heat Sunday morning from Bush, who said Cruz's promise to "carpet bomb" the Islamic State terrorist group was irresponsible considering the number of innocent lives that would be at stake. In the most recent GOP debate, Cruz clarified he would tailor the bombing to where the enemy is, not necessarily level entire cities. 

"We're going to destroy 800,000 lives with a carpet bombing activity? This is foolish. It is absolutely foolish," Bush said on CBS's "Face the Nation." "And he had to back away from it. It was kind of clumsy because he's a gifted speaker. It was a little unusual to see him stumble a bit."

Cruz has categorically dismissed such allegations of inconsistency by chalking them up to his growing dominance in the Republican race for the White House. On Sunday morning, another poll found him in the No. 1 spot in Iowa, beating Trump by 9 percentage points. 

Cruz's GOP rivals did not come up as he spoke with reporters Sunday afternoon before a rally near Birmingham, Alabama. Instead, Cruz kept the focus on the Democratic side, ripping frontrunner Hillary Clinton for her suggestion at a debate Saturday night that one of Cruz's Republican opponents, Donald Trump, is helping recruit members of the Islamic State terrorist group with his bombastic proposals. 

"It doesn't surprise me that Hillary Clinton is trying to find somebody to blame ISIS on," Cruz said, calling the group's rise a product of her tenure as secretary of state. "Naturally she's going to try to accuse a hotel developer in New York of being responsible for the chaos she created."

Cruz admitted, however, that he did not catch Clinton's comments on Trump on Saturday night. Instead, he said he went to see the new "Star Wars" movie, calling it "a reality that was far more realistic than whatever" was said at the Democratic debate.