"I'm confident we'll get there on the Republican side," Cassidy said, according to the Washington Examiner. "People are coming out and saying they are for it, either publicly or privately."
"Talking to a few more," Cassidy said, according to Vox.com
But similar optimistic comments by other senators in recent months about the prospects of previous Obamacare repeal bills have been proven wrong, badly.
Sen. John McCain, R-Ariz., in July dramatically voted no against a last-ditch, early morning effort by the GOP to pass a version of repeal.
Sen. Rand Paul, R-Ky., had voted for that prior bill. But the libertarian Paul on Friday cast cold water on the Graham-Cassidy bill.
Graham-Cassidy also could face the same opposition from two moderate Republicans, Sens. Susan Collins of Maine and Lisa Murkowski of Alaska, that with McCain's vote doomed late July's bill.
The latest bill, released Wednesday, would eliminate Obamacare's requirement that most Americans have some kind of health insurance or face a fine, and that large employers offer affordable health coverage to workers or pay a penalty.
And it would wipe out Obamacare funds that now subsidize the purchase of private health plans by millions of low- and middle-income people, and eliminate the expansion of Medicaid benefits to millions of poor adults.
In its place, Graham-Cassidy would award individual states block grants of money to craft their own health insurance system. But net federal spending related to support of health coverage would drop by many billions of dollars.
The bill has yet to receive an analysis by the Congressional Budget Office.
Previous CBO "scores" of the other Obamacare repeal bills found that they would lead to 20 million or more people lacking health insurance by 2026.
That big number spooked several GOP senators, and led to a widespread public backlash against the bills.
Graham-Cassidy is likely to receive a similar, or perhaps even worse CBO score in terms of the number of newly uninsured, given its design.
In an analysis posted Wednesday, the Center on Budget and Policy Priorities wrote that the bill "would have the same harmful consequences as those prior bills."
"It would cause many millions of people to lose coverage, radically restructure and deeply cut Medicaid, and increase out-of-pocket costs for individual market consumers," said the liberal think tank.
CBPP also noted that there would be an $80 billion reduction in the amount of federal money spent nationally on insurance support, and published a chart detailing the funding losses per state.
Despite that, defenders of Obamacare were taking very seriously the chance that the bill could pass, and sought to remobilize the kind of public opposition that helped defeat prior bills.
Among them was Andy Slavitt, who ran the federal Centers for Medicare and Medicaid Services under President Barack Obama.
Brad Woodhouse, director of the Protect our Care Campaign, in an email Friday blasted the Graham-Cassidy bill, but noted Republicans "are only a handful of votes away from passing it."
"Given Republicans will have to ram this partisan repeal bill through the Senate in the next two weeks in order to meet this September 30 deadline there will be no time for a regular process for the public to fully understand the impacts on their health care — with no time for adequate hearings, consultations with experts, constituent input, and amendments," Woodhouse wrote.
"Republicans in the Senate are resorting back to a secret, partisan process to force through health care repeal out of public view. The American people need to know the facts about how this bill will impact them. "
Sen. Ron Wyden, D-Ore., also took to Twitter to rally people to oppose the bill.
If the GOP does not pass the Graham-Cassidy bill, it is extremely unlikely that they will be able to approve any Obamacare repeal legislation before the midterm elections in 2018.
That fact could add some momentum to the latest repeal effort.