A group of Senate Republicans spearheading a rollback of the Affordable Care Act tried to persuade three skeptical but critical senators to support their efforts over the weekend — but were unable to extract any promises that would guarantee the embattled measure's success.

Sen. Bill Cassidy (La.), who introduced a revised version of his health-care bill earlier Monday, told The Washington Post in an interview that he mostly focused on tweaking the policy and left outreach up to two other Republican colleagues who helped craft the measure: Sen. Lindsey O. Graham (S.C.) and former senator Rick Santorum (Pa.).

Cassidy said Graham and Santorum facilitated conversations with Sens. Lisa Murkowski (Alaska), Susan Collins (Maine) and John McCain (Ariz.), whose states would receive more federal health-care funding under his revamped bill compared to a previous version.

[New GOP health-care bill in jeopardy as Sen. Rand Paul expresses opposition]

Murkowski and Collins, whose votes are crucial to the success of the Cassidy-Graham measure, have insisted that any attempt to replace parts of the ACA must not hurt their states. Asked whether he designed those changes with the two moderate Republicans in mind, Cassidy insisted that many states — not just Alaska and Maine — would benefit.

But he acknowledged that the new version would indeed provide more funding to those states compared to the first iteration of his bill, stressing that it would include $1 billion more in block grants for Maine. And he expressed hope that Collins would support the measure.

"If there's a billion more going to Maine . . . that's a heck of a lot," Cassidy said. "It's not for Susan, it's for the Mainers. But she cares so passionately about those Mainers, I'm hoping those extra dollars going to her state . . . would make a difference to her."

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The Louisiana Republican also suggested that Collins, who is considering running for governor in 2018, could help implement the measure if it passes.

"Imagine what a smart governor who knew health insurance so well as Susan does could do with that money to benefit lower-income Mainers," he said.

Cassidy-Graham has been met with sharp resistance from several GOP senators, and seemed headed for a collapse before a vote that Senate Majority Leader Mitch McConnell (R-Ky.) said he would hold this week.

Republicans can afford to lose the support of only two senators because of their slim 52-48 margin in the chamber, and time to deliver on a signature campaign promise is running short. On Saturday, special budget rules that allow them to pass health-care legislation without Democratic support will expire. President Trump has also urged Senate Republicans to pass the bill.

And Sen. Rand Paul (R-Ky.) said Monday morning that the changes to Cassidy-Graham aren't enough to persuade him.

Nonetheless, the Louisiana senator appeared exuberant that his measure has gained as much traction as it has, after Republicans failed to pass several other Obamacare replacement measures in July.

"Two years ago people thought I was Don Quixote. A month ago people thought things were dead. Two weeks ago, people smiled - and now folks say, 'Wow, they may still pull it off,'" Cassidy said. "If you keep your head down and keep plugging, good things happen."

Cassidy contended that naysayers like Paul should recognize that the new measure would save the country from the single-payer system that Sen. Bernie Sanders (I-Vt.) and some Democrats are pushing for.

"I'm hoping Senator Paul would kind of have that epiphany," Cassidy said.

The legislation would broadly convert federal Medicaid funding for expansion programs and subsidies for low-income Americans to purchase health insurance into block grants for states to design their own health-care systems. But the new state-by-state formula in the revised measure introduced Monday morning has some winners and losers, with Alaska gaining 3 percent more than it would have under the old bill; Maine securing 43 percent more; and Arizona receiving 15 percent in additional federal funding. The measure would redistribute federal health-care funding among all states, not just the ones that expanded Medicaid under the ACA.

Cassidy defended the new distribution of funding, saying conversations with the moderates were about "how do we hold your state harmless."

"All of this was designed to as much as possible hold states harmless while benefiting those non [Medicaid] expansion states where there are so many folks who would benefit if the state could afford to provide them better coverage," he said.

Cassidy said he's holding out hope that with the boosted funding — along with a Monday afternoon Senate Finance Committee hearing on the measure, where he will testify — Murkowski, Collins and McCain will ultimately vote for the bill.

"Our hope is that Maine gets a billion dollars more for four to five years, that we correct some problems that have been evident in Alaska. . . . We're having a hearing to vet these ideas that hopefully Senator McCain will say, 'Wait a second, we're having a hearing after all,' " Cassidy said.

McCain has complained about a lack of "regular order" — committee hearings, for instance — on major health-care legislation. He has said a single hearing isn't enough to satisfy his request.

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