As 2016 came to a close, Republican congressional leaders believed they had a basic idea of how they were going to repeal and replace Obamacare. But in the new year, this sense of a broad consensus has collapsed.

Some Republicans want a bill that will repeal all of Obamacare while others want to keep key aspects of it. They are fighting over how many people to try to cover, how much to spend, how much to tax, about the sequence of legislation, and when any sort of repeal would actually go into effect. And that's just in Congress.

President Trump, at various times, has called for a plan that spends less than Obamacare and covers more people, and with insurance that is cheaper, more comprehensive and with lower deductibles.

The biggest obstacle Republicans have to face is what to do with the millions of people who are currently receiving benefits through Obamacare as they devise a new system. Given the complexity and potential for political blowback, Matt Lewis has argued that Republicans may be better off giving up on the idea of repealing and replacing Obamacare and simply punting on the matter.

But Republicans owe their House and Senate majorities, and arguably the White House, to their vows to voters to repeal Obamacare. This is so core to what they have fought for, that surrendering now just because healthcare policy is hard, should not be seen as an acceptable option.

So what can Republicans do to make changes to system in as orderly a way as possible?

They should agree that whatever else is in their upcoming Obamacare bill, that it include one measure: a provision to freeze new enrollment in Obamacare. That is, they could continue allowing those who have benefits to receive them, but then prevent anybody from enrolling in the law's expanded Medicaid program who was not already on the books as of the date the bill is signed into law. Additionally, nobody would be eligible for subsidies for Obamacare's exchanges who did not already sign up for coverage by Jan. 31 — the last date of open enrollment for this year.

The current preferred approach of repealing much of Obamacare on paper, and then delaying the implementation of that repeal, creates a multitude of problems. One of them is that the program would be enrolling millions of new people into a system that is about to go away, meaning more people will be disrupted the longer Republicans wait. Even if Republicans were to limit a delay to under two years (that is, make the effective date Jan. 1, 2019) that would mean additional open enrollment cycles for the exchanges this fall and in the fall of 2018, let alone continued Medicaid enrollment.

It would also create an "Obamacare cliff" — a date at which subsidies would be cut off suddenly. If past behavior of Congress is any indication, it's quite possible that lawmakers, urged on by Trump, could end up delaying the delay. If they don't want it to go into effect leading up to the 2018 elections, would Republicans want it to go into effect as the 2020 presidential election approaches, especially if they may be working with a reduced Congressional majority?

By freezing enrollment, the number of Obamacare beneficiaries would dwindle due to attrition as people who have insurance on the exchanges or through Medicaid move onto other coverage, such as employer-based insurance. There is precedent for this with Medicaid.

In 2000, Arizona expanded Medicaid, but quickly found that it was facing cost overruns. The state responded by freezing enrollment. Within a year, according to a study from the Foundation for Government Accountability, 49 percent of enrollees had left the expanded program; by the end of two years, 67 percent had exited.

A freeze, thus, would be allowing benefits to flow to current beneficiaries while moving more and more individuals off of Obamacare dependence over time.

During this transition period, Republicans could work on a replacement mechanism to provide different options to help people purchase insurance — whether this be in the form of tax credits, high-risk pools, deductions, or large health savings accounts.

Once those options go into effect, it would speed up the exodus from Obamacare, as people receiving Obamacare subsidies migrate by themselves.

Under this scenario, when it comes time to pull the plug on Obamacare for good, far fewer people would be disrupted by any change, and if handled properly, a new system would have already been up and running.

For conservatives, this approach also provides a form of insurance against the possibility that Republicans will keep punting on repeal for years, until it never actually happens. Under the freeze scenario, even if Republicans keep delaying the date for repealing Obamacare indefinitely, by the end of Trump's four-year term, the size of Obamacare would have shrunk substantially.

Even the relatively simplest path to repealing Obamacare, of course, is not east or without its obstacles. But whatever their differences, Republicans broadly agree that the healthcare system, as it exists under Obamacare, needs to change. Wherever they are on the spectrum of opinion over replacing it, they shouldn't in good conscience allow people to continue enrolling in a system that they're trying to eliminate.