The Senate's budget resolution, which includes the rules for ObamaCare repeal, gives senators until late January to come up with legislation to nix the Affordable Care Act. Under a proposal from five GOP senators, including Corker, they would have had until Mach 3. 

The budget resolution is expected to pass late Wednesday or early Thursday. 

Corker and Sen. Rob Portman (R-Ohio) signaled on Wednesday night that Senate GOP leadership was open to giving lawmakers more time to work out a repeal legislation beyond the January deadline. 

"Everyone here understands the importance of doing it right, giving Tom Price, the new [Department of Health and Human Services] person, the time to weigh in and help us make this work in the appropriate way," he said. 

Portman added that "we have assurances from leadership ... that this date is not a date set in stone." 

"It is the earliest we could do it but could take longer and we believe that it might," he said. 

It's unclear if the GOP senators had enough support to pass their amendment. 

Sen. John Cornyn (R-Texas), the Senate's No. 2 Republican, warned on Tuesday that delaying the repeal legislation could lead to a "jam" on the Senate floor. 

"I don't think we should delay it any more than we have to because we have a second budget resolution that we want to pass to get reconciliation instructions for tax reform," he said.

Sen. Lindsey Graham (R-S.C.) separately voiced skepticism on Wednesday, saying repealing ObamaCare through reconciliation had a "shelf life."

Republicans have been publicly divided about how to repeal and replace ObamaCare. 

President-elect Donald Trump said during a press conference on Wednesday that repeal and replace would move near simultaneously if not at the same time. 

“It'll be repeal and replace. It will be essentially, simultaneously. It will be various segments, you understand, but will most likely be on the same day or the same week, but probably, the same day, could be the same hour,” he said.

But Graham — whom Trump mocked during the press conference — told reporters that the president elect “needs to call Mitch McConnell because that's not where we're headed.”

Republicans plan to use the reconciliation process to repeal Obamacare which means they can pass it with only a simple majority.  The repeal will almost certainly come in stages, given the enormous complexity of the law, which touches on budget, tax, and regulatory issues all at the same time.

It is still unclear what route the GOP will take in replacing Obamacare.  Certainly, some of the more onerous parts of the law, like the individual mandate and mandated coverage for birth control and mental health services that need to be in every insurance policy will be repealed outright. 

But other parts of Obamacare, like the rule that forces insurance companies to charge the same for premiums bought by patients with pre-existing conditions will likely be reformed, rather than repealed.  There is also a possibility that some form of Medicaid expansion will remain on the books.

Some hardship for consumers is inevitable.  But the replacement bills will look to limit the impact on the insurance industry and consumers – or at least, institute a phased in reduction in some benefits to lessen the blow.

The only thing that really matters is that the Republican Senate is on board for repeal of Obamacare and there's nothing the Democrats can do to stop it.