Republicans in the House plan to hold a vote in January to repeal President Barack Obama's healthcare overhaul and say they have nearly enough support to override a presidential veto of the repeal, a top lawmaker said Sunday.

"Unpopularity numbers are as high as 60 percent across the country," Fred Upton, the incoming chairman of the House Energy and Commerce Committee, said of the healthcare law.

"I don't think we're going to be that far off from having the votes to actually override a veto," Upton said on "Fox News Sunday."

Democrats contend Republicans are wasting Congress' time by staging a healthcare repeal vote, saying it will die in the Democratic-controlled Senate.

But Upton said a big House vote for repeal could sway votes in the Senate "to perhaps do the same thing. But then, after that, we're going to go after this bill piece by piece," he said, by trying to block various parts of the law including an individual mandate for insurance coverage.

"We will look at these individual pieces to see if we can't have the thing crumble," Upton said.

But Representative Debbie Wasserman Schultz, a Democrat, said on CBS' "Face the Nation" people are learning more about benefits of the healthcare law, diminishing chances it will be defeated.

"A constituent in my district came up to me a few weeks ago and thanked me for saving her $3,000 a year because she could put her two adult children back on her insurance. That's what the Republicans are going to be proposing to repeal this week. It's not going to happen," she said.

"I think you're going to see the fight on Obamacare across the board in the House and the Senate to try to defund the Obamacare bill and to start over," Republican Senator Lindsey Graham said on NBC's "Meet the Press."

Graham said he would work "to allow states to opt out of the individual mandate, employer mandate and expansion of Medicaid."