Sen. Lindsey Graham said Sunday that the latest cost estimates for Democrats' health care overhaul amount to a "death blow" to calls for a government-run plan. 

The influential South Carolina Republican was responding to estimates this past week from the Congressional Budget Office, which tagged one plan at $1.5 trillion over 10 years and another at $1 trillion over 10 years. Though many experts anticipated a comprehensive health care overhaul would cost about $1 trillion, the CBO predicted that the latter plan would only cover 16 million uninsured -- or about one-third of those who currently lack coverage. 

Graham said the estimates mean that a government-run plan, which many Democrats view as critical to health care reform, cannot be part of negotiations. 

"The CBO estimates were a death blow to a government-run health care plan," Graham said, adding that there's been a "bipartisan rejection" of such an idea. 

"This idea's unnerving to the members of the Senate," he said on ABC's "This Week."  "I think this idea needs to go away." 

Sen. Chris Dodd, D-Conn., who is trying to shepherd through one of the health care reform bills, said a public plan is the only way to bring down skyrocketing costs in the long run. He insisted, as President Obama often does, that the public plan would stand as just one option among many for the public -- anyone who wants to keep their private plan would be able to under the proposal. Dodd objected to the way the public plan was being described by critics. 

"I don't think you can bring down costs without it," Dodd said. "We use a lot of these buzzwords. No one I know is for socialized medicine. We're going to develop a U.S. plan, not a Canadian or U.K. plan -- one that meets our needs and our country, that's designed for America by Americans. It isn't socialized medicine, but you've got to drive down these costs." 

Dodd said senators will work to bring down the cost of a health care reform program and ensure that it covers more people, and said lawmakers are only at the beginning of negotiations.