Sen. Rand Paul (R-Ky.) walks to the Senate chamber on Capitol Hill in Washington for a vote Tuesday. (J. Scott Applewhite/AP)

The embattled Republican effort to repeal the nation’s health-care law now centers on winning over a hard-line conservative, Sen. Rand Paul (R-Ky.), who continues to engage with President Trump and Senate leaders, giving proponents of the latest GOP bill a glimmer of hope.

While Paul remains wary of that proposal, he signaled Sunday that he is willing to consider a “narrow” version of the legislation, which would give states vast authority over money provided under the Affordable Care Act and waive many federal rules and regulations.

Paul said he broadly opposes a keystone of the Republican plan: issuing “block grants” to states to use federal funds being spent on Medicaid expansion and subsidies as they wish. But he is willing to hear out suggestions about how that aspect of the bill could be constricted.

“Would I talk to them if they said they wanted to make the block grants half as much? I might,” Paul said in an interview on Sunday. “But I’m afraid you get back in the box where the moderates want more and the conservatives want less.”

Paul’s attempts to shrink the bill’s scope could present new challenges for the legislation, which moderate Republicans have been reluctant to back. Still, the Kentucky senator is confident that the White House and his colleagues must work with him to have a chance at passage and fulfill a party promise.

Sens. Susan Collins (R-Maine) and Rand Paul (R-Ky.) listed their concerns on Sept. 24 about a health-care bill sponsored by Sens. Bill Cassidy (R-La.) and Lindsey O. Graham (R-S.C.). (Bastien Inzaurralde/The Washington Post)

“Do they want to just give up and not do anything? Maybe. Maybe they go forward and don’t bring up anything,” Paul said. “Otherwise, it’s time to bring up a smaller, more narrow bill and see if they can get the votes.”

Paul’s turn in the spotlight and bid to steer the negotiations comes after Sen. John McCain (R-Ariz.) announced last week that he could not “in good conscience” vote for the stalled Republican bill written by Sens. Bill Cassidy (R-S.C.) and Lindsey O. Graham (R-S.C.).

And Sen. Susan Collins (R-Maine) told CNN’s “State of the Union” on Sunday that it would be “very difficult” for her to support the bill, leaving Republicans, who hold a 52-seat majority, little room for further defections.

Paul, an ophthalmologist, said the obvious next step for Republicans would be to bring up a bill that includes provisions that he believes have support in the GOP cloakroom: capping taxpayers’ expenditures on Medicaid spending and giving states control, curbing regulations and allowing people to join health associations where they could purchase out-of-state insurance plans.

“All of those could be in a bill, and you could pass that. They’re going to have to decide whether they’re willing to do that without block granting,” Paul said. “The problem I have with block grants is that looks like I’ve affirmatively said I’m okay with 90 percent of Obamacare as long as we reshuffle it and give it to Republican states. That’s a horrible message.”

But Paul cracked the door open to providing some funds to states if the amount of money was significantly reduced from the levels under Cassidy-Graham.

“Nobody has really offered me that, to say, ‘Well, we could spend less,’ ” Paul said. “But we’re going to have a $700 billion deficit, and this is an entitlement program.”

Paul’s push to roll back the size of federal spending on health care in the bill could spark debate even among Republicans — especially those worried about their states’ poor losing out on federal money provided under current law. Collins and Sen. Lisa Murkowski (R-Alaska) have voiced such concerns.

“They’ve got to talk to Collins and Murkowski about whether there is any Medicaid cap they can live with,” Paul said. “Find what they can live with, and you’ve got a narrower bill.”

An internal analysis by the Trump administration recently concluded that 31 states would lose federal money for health coverage under the Republican plan. That report, produced by the Office of the Actuary within the federal Centers for Medicare and Medicaid Services, focused on the final year of a block grant that states would receive under Cassidy-Graham and showed that government funding for health insurance would be 9 percent lower overall in 2026 under the plan than under current law.

The method used by federal officials to predict the bill’s effects on spending to states differs from that of another major analysis released earlier last week by the Kaiser Family Foundation. The latter concluded that 35 states would lose $160 billion under Cassidy-Graham.

Paul said he worked closely with the White House over the weekend to discuss the details of potential changes to the Cassidy-Graham bill and is in touch with Graham.

“They’re pleasant conversations,” Paul said. “They know if they want me, they’re going to have to make the bill more of a repeal bill and less of a ‘we’re going to divvy up the pie to Republicans’ bill.”

Paul also dismissed the notion that he could be convinced to back Cassidy-Graham if he was promised something on another front that nodded to his libertarian positions on matters of military action, where he routinely pushes for more congressional oversight.

“I’m not going to trade my vote for something ancillary or be bribed,” Paul said.

In a new Washington Post/ABC poll, just 33 percent of voters said they supported the Cassidy-Graham plan, making this last dash at repeal a political burden as well as a whipping test.

“It is very difficult for me to envision a scenario where I would end up voting for this bill,” Collins said on CNN. “I have a number of serious reservations about it.”

Amy Goldstein and Juliet Eilperin contributed to this report.