McCain's potential support of the Graham-Cassidy bill is significant because he was one of just three Republican senators whose opposition to a prior GOP-sponsored Obamacare repeal bill doomed it in July.
The other "no" votes came from Susan Collins of Maine, and Lisa Murkowski of Alaska.
If McCain does end up voting for Graham-Cassidy, GOP leaders may need to convince only two other Republican senators to back the bill to guarantee its passage. (The prospective gain of McCain's "yes" vote would be canceled out by Sen. Rand Paul, R-Ky., who plans to vote "no" on Graham-Cassidy — despite having voted for the prior repeal legislation in July).
Murkowski reportedly said Monday that she is undecided on Graham-Cassidy.
When MSNBC correspondent Garrett Haake asked McCain on Monday if he would vote for Graham-Cassidy, the senator replied:
Ducey wasted no time weighing in with his opinion on the bill.
Despite Ducey's endorsement of Graham-Cassidy, it is far from a done deal that McCain ultimately will support the legislation.
One factor that could sway McCain back in the other direction is an analysis that finds Arizona would lose $1.6 billion in federal health funds if Graham-Cassidy becomes law. The analysis was published by the Center on Budget and Policy Priorities, a liberal think tank.
Sen. Bill Cassidy, R-La., one of the sponsors of the bill, last Friday said there were up to 48 or 49 Republican senators who supported the bill. Cassidy did not identify who among the 52 Republicans in the Senate are not backing the bill as of yet.
GOP leaders need at least 50 votes for the bill to pass, presuming a tie-breaking vote from Vice President Mike Pence, who is a Republican. No Democrat or independent is expected to vote for the bill.
Paul on Monday said there is no chance he will be one of those 50.
"I promised people repeal, this has nothing to do with repeal," Paul said.
"This is keeping Obamacare, redoing the formula to give Republican states more money," Paul told reporters. "I mean, that's as simple as it gets."
Paul also said that he thought that the Obamacare repeal effort was finished, at least in the short term.
"I like most people thought it was completely dead and gone, buried, and there wasn't going to be any more attempts," he said. "I'm kind of surprised that this has been resurrected because I don't think it has been fully thought through, I think it's actually more complicated than some people make it out to be."
The bill has to be passed by Sept. 30 if it is to become law, because the GOP is using a procedural process known as reconciliation to expedite its approval.