Republicans are planning to push for a repeal of Obamacare's individual mandate that requires people to buy health insurance or pay a fine, either through a bipartisan healthcare bill or through a tax plan.

"Almost every colleague with whom I have spoken is favorably disposed toward repealing the individual mandate of Obamacare as part of that tax package," Sen. Tom Cotton, R-Ark., told reporters.

The individual mandate is one of the most unpopular parts of Obamacare. The Supreme Court in 2012 upheld its provisions, saying the mandate was constitutional because of the government's power to tax. Chief Justice John Roberts joined four left-leaning judges to cast the majority decision.

Sen. John Barrasso of Wyoming, the Senate's fourth-ranking Republican, told reporters that he supports repealing the individual mandate and that it could be included in a bipartisan bill that would help stabilize Obamacare.

"I'd love to see the individual mandate repealed, period," he said. "I think it's unconstitutional. I know that Justice Roberts said it wasn't, that it was a tax. But I disagree with the Supreme Court decision on that."

"I'd like to have it included in lots of different options," he continued.

The White House also has asked that repeal of the individual mandate be included in the bipartisan bill, and its repeal would be similar to the "skinny repeal" bill that Republicans failed to pass on Obamacare this summer.

Cotton said he had been "working for some time now" with members of the Senate Finance Committee and the House Ways and Means Committee to include the individual mandate in the tax package. If it does not make it into the text of the bill, Cotton said, he would work to add it through committees or on the Senate floor through amendments.

The House is expected to roll out a tax package Wednesday.

Not all GOP senators appeared to agree with Cotton's suggestion. Sen. Ron Johnson, R-Wis., one of the backers of a bill that would have overhauled Obamacare, which became known as Graham-Cassidy, said, "I think you've got to take care of tax reform first."

Experts disagree on the effectiveness of the individual mandate to get people signed up for health insurance coverage, saying that it wasn't strong enough to get people to sign up and that affordability and pre-existing illnesses tend to dictate a person's decision to buy coverage. Proponents of the mandate say that some impetus is needed to bring healthier people into the insurance pools to help balance out the medical claims of more costly enrollees.

Cotton pointed out that the Obama administration allowed for a range of exemptions to the individual mandate, a move critics said adversely harmed the exchanges.

A Congressional Budget Office report found that if the individual mandate were repealed, 16 million more people would be uninsured.

• Al Weaver contributed to this report.