Senate Republicans want to box majority Democrats into allowing a health care repeal vote even if GOP lawmakers expect to be on the losing side.
"We need to have a vote on it because we promised the people we would," Sen. John McCain, R-Ariz., said Sunday on Face the Nation on CBS.
Republicans took control of the House after November's elections and last week voted, as promised, to repeal the health care law. Only three Democrats joined all Republicans in the 245-189 vote to scrap the law.
In the Senate, Democrats retained majority control.
While Majority Leader Harry Reid, D-Nev., who controls the Senate agenda, has said such a bill won't come to a vote, Republican leader Mitch McConnell repeated his promise that a repeal vote will indeed take place.
"I'm not going to discuss how we'll do it from a parliamentary point of view here," McConnell said on Fox News Sunday.
"If that does not pass, and I don't think anyone is optimistic that it will, we intend to go after this health care bill in every way that we can. It's the single worst piece of legislation that's been passed in my time in the Senate," McConnell said.
One route to a repeal vote could be through an amendment brought to the Senate floor, according to Sen. Dick Durbin of Illinois, the No. 2 Democrat.
"If some Republican senator wants to offer it as an amendment at some point, it's possible they will. It's possible we'll face that vote," Durbin said on Fox. "But having spoken to my members in the Democratic caucus, with Sen. Reid, we feel there's still strong support for health care reform."
Only about one in four people say they want to do away with the health care law completely, according to a recent Associated Press-GfK poll.
For those reasons, Sen. Chuck Schumer, D-N.Y., suggested that Republicans should be careful what they wish for.
"If the Republicans offer an amendment on the floor, then we will require them to vote on the individual protections in the bill that are very popular and that even some of the new Republican House members have said they support," Schumer said on CBS. "So, in the end, their repeal bill is going to be so full of holes it looks like Swiss cheese."