President Obama's top political adviser accused Mitt Romney of having "no core," saying Wednesday that the former governor running from his record on health care in Massachusetts is the reason he's hit a ceiling in Republican support for the presidential nomination.

David Axelrod said Romney, who has steadily drawn about 25 percent in national polls while his opponents rise and fall around him, is struggling to consolidate more Republican support because "there's a sense that there's no core to him." 

Axelrod cited the health care program Romney signed into law as governor of Massachusetts, which Romney has to own in the face of strong GOP opposition while repeatedly saying he would not introduce as a national plan.

"We modeled our health care program largely on what he did in Massachusetts," Axelrod told CBS' "Early Show." "Now he says I never intended it be a model for the nation. In 2007, he said this would be a model for the nation. And time and time and time again, Gov. Romney switches from one position to another."

Romney campaign spokeswoman Andrea Saul lashed back at Axelrod, calling his comments "ridiculous."

"Of course he's going to try to distract from his record of failure on this economy," she told Fox News. "And Axelrod's comments are patently false. Governor Romney has been clear and consistent that he would never have a one-size-fits-all health care plan for the entire nation.

"And he's going to repeal Obamacare once he's in office, on Day One, giving waivers to all 50 states so they can get out from under the burden of this huge government program."

Romney's Republican rivals seized on his state's health plan in a debate Tuesday night in Las Vegas. 

Former Pennsylvania Sen. Rick Santorum repeatedly hit Romney on his support for the state overhaul, which included a provision requiring people to get health insurance much like the federal health care law.

"What you did is exactly what Barack Obama did, focused on the wrong problem," Santorum said. "What you did with a top down government-run program was focus on the problem of health care access. You expanded the pool of insurance without controlling costs. You've blown a hole in the budget up there, and you've authored in Obamacare, which is going to blow a hole in the budget of this country."

Former House Speaker Newt Gingrich said comparing Romney's plan to "Obamacare" is not a "fair charge." 

But he added, "Your plan essentially is one more big government, bureaucratic, high-cost system, which candidly could not be done by any other state because no other state had a Medicaid program as lavish as yours. And no other state got as much money from the federal government under the Bush administration for this experiment, so there's a lot of big government behind Romneycare -- not as much as Obamacare, but a heck of a lot more than you campaign is admitting."

Romney responded to Santorum that "the people of Massachusetts like" their health care by a 3-1 margin, even if the costs for it haven't risen more rapidly than in other states.

"It's absolutely right that there's a lot that needs to be done. And I didn't get the job done in Massachusetts in getting the health care costs down in this country. It's something I think we have got to do at the national level. I intend to do that," he said.

"But one thing is for sure. What Obama has done is imposed on the nation a plan that will not work, that must be repealed. And when it comes to knowledge about health care and how to get our health care system working, I may not be a doctor ... but I sure understand how to bring the cost of health care down and how to also make sure that we have a system that works for the American people."

Texas Gov. Rick Perry also attacked Romney on immigration, resurrecting a charge from the last presidential campaign that Romney hired illegal immigrants to landscape his property.

Romney acknowledged that the lawn company he hired had employed illegal immigrants.

"So we went to the company and we said, look, you can't have any illegals working on our property. I'm running for office, for Pete's sake, I can't have illegals," he said, adding that he eventually fired the contractor.

Axelrod called that exchange a "revealing moment" because Romney cited his presidential bid in his opposition to hiring illegal immigrants.

"Not 'it was wrong,' not 'it was illegal,' but, 'I'm running for office,'" Axelrod said. "I thought that was the most unintentionally revealing moment of the debate."