In recent days, a number of Republican senators, particularly Maine's Susan Collins, have pushed the idea of approving so-called reinsurance funding for Obamacare as part of a deal that would repeal the law's individual mandate. That mandate requires most people to have some form of health insurance or pay a penalty.
Collins opposed the idea of including repeal of the mandate in a pending Senate tax bill supported by GOP leaders, who are still struggling to attract the 50 Republican votes needed for passage. A House version of the tax bill does not include the mandate repeal.
But on Tuesday, she told Politico that "If it [the mandate's repeal] is going to be included it's essential that we mitigate the impact on premiums."
"That includes passing the Alexander-Murray bill and also a bill that I have with Bill Nelson that would protect people with pre-existing conditions. And yet lower premiums through the use of high risk pools," Collins said.
Collins' bill calls for allocating $4.5 billion over two years to fund state reinsurance programs. Those programs would subsidize the cost to Obamacare plans from customers who have heavy medical needs.
That, in turn, could reduce, or eliminate increases in premiums that would result from repeal of the individual mandate.
The Congressional Budget Office has estimated that repealing the mandate would lead insurers to tack on an extra 10 percent increase in premium prices each year — beyond the normal year-to-year price hikes.
The other part of Collins' proposal is passing the Alexander-Murray bill, which would restore billions of dollars in federal reimbursements to insurers to compensate them for discounts in out-of-pocket charges they must grant, by law, to low-income Obamacare customers.
Larry Levitt, an Obamacare expert with the Kaiser Family Foundation, told CNBC that "Alexander-Murray, as it's currently drafted, wouldn't really do anything to mitigate the effects of repealing the individual mandate."
But funding reinsurance programs "could offset any premium increase" resulting from repeal, Levitt said.
Totally offsetting such price hikes from repeal would require some additional funding, and extending reinsurance beyond the two-year span outlined in Collins' bill, he said.
However, "it wouldn't do anything to deal with the fact that more people are likely to be uninsured" as a result of the mandate's repeal, Levitt said.
If the mandate is repealed, the CBO estimates that 13 million more people would become uninsured by 2027 than are currently projected.
"Most of the losses [in insurance coverage] are due to the fact that people are not getting pushed into getting coverage," Levitt said.
Earlier this year, a series of Republican proposals to repeal and replace major parts of Obamacare failed to pass Congress — and were broadly unpopular with the general public — in large part because they were projected to lead to big drops in the number of Americans with health insurance.
Sen. Patty Murray, D-Wash., who co-authored the Alexander-Murray bill, told The Washington Examiner, "I support reinsurance, but it won't solve the problem they created," referring to the mandate repeal.
"The bill we designed has not been written to block the premiums they're creating," Murray said.
Republican lawmakers as a group are less likely to be concerned with the increase in the number of uninsured people.
"The premium increases on middle-class consumers is probably the most troubling part of repealing the individual mandate, particularly for Republicans," Levitt said.
Many middle-income Americans earn too much to qualify for Obamacare subsidies that lower monthly premiums. That means those people bear the full brunt of premium increases.