Republican health-care proposals don't address the real problems and could potentially wind up being "very destructive" to large hospitals in urban areas, Mount Sinai Health System CEO Dr. Kenneth Davis told CNBC on Thursday.

GOP leaders are still trying to garner enough votes to pass their bill in the Senate, while others in the party are putting forward their own ideas.

"We're going to be losing an awful lot of Medicaid and that's going to provide the hospital systems with lots more patients with uncompensated care," Davis said in an interview with "Closing Bell."

Plus, people with pre-existing conditions will also find they can't afford their policies, he said.

"The hospitals by law are going to have to take care of them and it's going to be very difficult to see how a lot of hospitals that already have very small margins are going to survive in that environment. We are fundamentally not dealing with the basic problems in health care by these bills."

Senate Majority Leader Mitch McConnell told Kentucky voters on Thursday that he's still grappling with getting enough votes for passage.

"I'm in the position of a guy with a Rubik's cube, trying to twist the dial in such a way to get at least 50 members of my conference who can agree to a version of repealing and replacing" Obamacare, he said.

Meanwhile, Sen. Ted Cruz, R- Texas, and Sen. Mike Lee, R- Utah, are circulating the "Consumer Freedom Option." The amendment would let insurers offer at least one Obamacare-compliant plan on a state's exchange, which would cover pre-existing conditions and get funding from tax credits and stability funds. "Freedom plans" would also be offered for healthy, young people.

Davis said the problem with that proposal is it takes healthy people out of the risk pool.

"As a consequence we are leaving behind in that comprehensive policy those people with pre-existing conditions, chronic disease or people who think they are at risk for illness," he said. "Those policies are going to be terribly expensive because you don't have the healthy people in those pools to bring down premiums."

He believes the issue of the high costs of health care need to be addressed.

"That means we have to change the way we deliver care," Davis said.

He proposes moving from fee-for-service toward a system where care providers are paid to manage a group of patients ahead of time.

"If they manage those patients efficiently, they're going to have some margin. If they manage them inefficiently, it's their loss," Davis said. "We've got to change the way health care is delivered. These bills are not addressing those questions."

CNBC's Kayla Tausche contributed to this report.

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GOP health-care bill not addressing problems, could be 'very destructive': Mount Sinai CEO - CNBC