Graham argued that the House bill was "written for liberals, by liberals.
"Just look at how it passed; it passed 220 to 215. It passed by two votes. You had  Democrats vote against the bill," Graham told "Face the Nation" host Bob Schieffer Sunday.
He also admitted that if it were to come down to it, he would join his independent colleague Senator Joe Lieberman, I-Conn., in filibustering a bill including the so-called public option should it come to the Senate floor.
"The House bill is a non-starter in the Senate," he added. "I just think the construct out of the House and what exists in the Senate is not going to pass, and I hope and pray it doesn't because it would be a disaster for the economy and health care," Graham concluded.
Graham believed a public option would "destroy" private health care, saying that insurance companies could not compete against the lower premiums of a government-backed plan. "It will be a death blow to private choice," he said.
Schieffer asked Senator Jack Reed, D-R.I., whether he believed that Senate Democrats had the votes to pass the House bill considering it includes the so-called public option.
"I believe we are going to pass health care reform," Reed responded. "I believe we must do this because it's essential to not just the quality of life here but our economic success in the future.
"Senator Reid, Harry Reid has introduced the public option and there is strong support there. but we are far from the end of the debate in the Senate. It will take time. It will be careful, thorough and deliberate.
"I hope that a public option is in the final bill," he added.
Reed admitted that there is an "active debate" taking place among senators and various provisions to a public insurance plan, such as the trigger option or allowing states to opt-out.
"Overwhelmingly, sixty percent of the American public want a public option and I think we should be listening to them as much as listening to ourselves," Reed said.