"This was a terrible bill," McConnell said on "Face the Nation" Sunday.
McConnel said the results of Election Day meant that "People who supported us - political independents - want it repealed and replaced with something else. I think we owe it to them to try," McConnell said.
Also on the program, House Majority Whip James Clyburn, D-S.C., defended the sweeping health care legislation, likening the reform with other major initiatives, like the civil rights laws of the 1960s. "The fact of the matter is what we did with health care is to make that a fundamental right of every citizen."
Clyburn suggested that McConnell and the House Republicans who say they will repeal the bill as soon as they take over the Majority leadership in January reminded him of the South's efforts to repeal landmark civil rights legislation.
"I think that those people who are saying those things are really flying in the face of history," Clyburn said. "The Democrats lost [their] place in the South because of the Voting Rights Act of 1965," Clyburn recalled. "I remember [former Republican Senator] Strom Thurmond going back to Washington after 1968, saying, 'We are going to repeal the Voting Rights Act.'"
And, Clyburn so much as dared the Republicans to try.
"I would like to see which one of those Republicans would propose that we take away a person's family's right to have their child [who's] born with diabetes come off their insurance policies," Clyburn said.
Host Bob Schieffer pointed out to McConnell that his fellow Republicans who would face President Obama's veto pen have an additional strategy: "They realize you can't repeal health care reform immediately. In the meantime what they would like to do is stop funding for some of the health care proposals."
Schieffer said some Republicans have proposed to dry out the health care bill. For instance, they would limit money and personnel to the Internal Revenue Service so that the agency will be unable to enforce provisions that require people to obtain health insurance, and for employers to pay for it.
Schieffer asked McConnell if he would be for that.
"Yeah, what we're doing in my office is looking for the various parts of it that are subject to funding. We will be revisiting this issue time after time," he said.
McConnell said he believes "the vast majority of Americans feel very, very uncomfortable with this new bill," and it was a major reason why the Democrats lost many seats in the House during Tuesday's midterm elections.
"We've got an obligation to those who gave us more authority in the Congress than we had last Congress to try," he said. "It will be difficult with the President there. I know he feels that this was his signature accomplishment. But I don't think we can simply ignore the commitments we made to the American people to try to repeal it and replace this."
Exit polls on Election Day showed that while 48 percent said they supported repealing the overhaul, 47 percent said it should be kept - or even expanded.
Clyburn accused the Republicans of lying about the health care bill during the campaign, charging that the GOP spent a lot of money on TV to instill fear that the bill would cut Medicare benefits for seniors.
"We were not cutting their services. We were cutting in those areas where there was so much fraud in existence," Clyburn said.