If opponents of Obamacare were to succeed and the president's health-care law collapsed, what would take its place?

Former Gov. Ed Rendell predicted Monday that a system like Medicare for everyone would emerge. "If Republicans and some Democrats who are attacking Obamacare have their way and Obamacare falls off, I think we're looking at single-payer down the road," the Pennsylvania Democrat told CNBC's "Squawk Box."

In a single-payer system, a single entity—usually a government—collects all fees for health care services and pays out all costs.

Also on the show, Republican Judd Gregg claimed a single-payer approach was the plan from the start. "You will have folks moving employees into exchanges, because why should they pay the full cost of insuring employees when they can put the cost on the exchange? And the exchange puts it on the taxpayer," the former New Hampshire senator and governor said.

"Then the exchanges can't function, because they won't be able to be subsidized at that level they have to be subsidized at," he continued. "Then you have the human cry that the only way we can solve this is with a single-payer."

Rendell said he did not support the single-payer approach, but added that if he had designed a system like that, it would be like Medicare. "We can have single-payer plus. A baseline that covers everyone and gives everyone prescription." People also would have the option to "buy up" for more robust coverage, he added.

A single-payer structure would lead to rationing," said Gregg. "You go to Canada, you're chances of getting elective surgery that's significant like hip replacement … you're going to have to wait two or three years. So you come to the United States and have it done." Sticking with the Canada example, Rendell pointed out that Americans turn to pharmacies north of the border to buy cheaper prescription drugs.