But other plans that need approval by Congress would still require 60 votes in the Senate, since only part of the original health law was approved under reconciliation by Democrats back in 2010.
While waiting to figure out the procedural process, some Republicans made clear they had no problem voting to repeal the health care system early in the year, and then later hashing out what should replace it.
"Sure, absolutely, it's collapsing of its own weight right now," said Sen. David Perdue (R-GA), "The quicker we do that (repeal), the quicker we get on to what we're going to do to fix it."
"It's not a total repeal - let's get that out of the way - it's a partial repeal," Perdue told reporters. "I think there are pieces of it in there that have to stay in place for a while, and that's what we're going to be working on.
That idea was echoed by the number two Republican in the House, Majority Leader Kevin McCarthy (R-CA), who also said the best course may be repeal - then figure out what should be done to replace the system.
Down at the White House, the outgoing administration raised some red flags about the effort, once more noting that Republicans have had six years to bring their own replacement plan to a vote in the House and Senate, but have never done so.
"What is clear is that the President-Elect has chosen to nominate someone who is an ardent opponent of the Affordable Care Act," said White House Press Secretary Josh Earnest.
"And we'll see how it measures up," Earnest told reporters.
One thing remains clear in Congress - saying you want to repeal and replace the Obama health law is one thing - doing it, is another.