Sen. Lisa Murkowski (R-Alaska) is trailed by members of the media in the basement of the Capitol on Tuesday.

Lisa Murkowski walked briskly down a cavernous hallway on the first floor of the Capitol, awash in a small sea of reporters. Suddenly she paused, seemingly overcome by the pressure of the moment.

“You guys — hold,” the Republican senator from Alaska said curtly. “Give me breathing room, please. It gets a little intense. I know you guys don’t feel it, but it’s like, whoa.”

Another effort to replace the Affordable Care Act is underway, and in Washington that means one thing: Murkowski is at the center of it all — under the glare of the national spotlight and squarely on the minds of White House officials and Senate Republican leaders who are strenuously seeking her support.

That’s the way it was Wednesday, as Sens. Bill Cassidy (R-La.) and Lindsey O. Graham (R-S.C.) huddled with Murkowski to sell her on their bill. Afterward, she said she was still not convinced. And Graham dismissed the notion of altering the bill just for Alaska.

What was clear by the end of the day was that if Republicans want Murkowski’s vote, they must either provide data showing that the legislation does not harm her state — a difficult task, given its outlines — or make changes that protect it.

Speaking at the United Nations, President Trump said the Cassidy-Graham health-care bill was likely to pass on Sept. 20. (The Washington Post)

Also clear was the very real possibility of a vote. Senate Majority Leader Mitch McConnell’s spokesman said he intends to bring the proposal to the Senate floor next week. And President Trump said the bill had a “very good chance” of passing.

After leaving the meeting with Cassidy and Graham, Murkowski said she needed to review more information on how the plan would affect her state before she decides whether to endorse it.

“I have asked for nothing except the data that we’re going to need to better understand the impact to a high-cost, low-density state like Alaska,” Murkowski said. She said she was seeking numbers from the Centers for Medicare and Medicaid Services and the Department of Health and Human Services, “working with our state’s Medicaid directors.”

Following the gathering, Graham said he and his co-sponsors would not make any changes to the legislation for Alaska. But he also sought to project sensitivity to the state’s distinctive needs, perhaps opening the door to some provisions that accomplish that.

“What we’re going to do is not deny Alaska the uniqueness of Alaska, but that’s it,” he added, after mentioning the state’s high medical costs.

Murkowski is one of at least four Republicans who remain unsure whether to support the legislation. But there is another reason the public’s attention tends to lock onto this warm yet resolute and sometimes brusque senator: No one has any idea what she will do.

Senate Republicans are trying to revive the momentum to overhaul the Affordable Care Act with the Cassidy-Graham proposal. Here's a rundown of the plan, and the rush to pass it. (Jenny Starrs/The Washington Post)

Like the state she represents, Murkowski projects an independent streak. She regularly breaks with her party — yet she is also willing to play ball. Alaska is mysterious and complicated. So is its senior senator.

“The problem last time was process and substance,” Murkowski said Tuesday after her pause in the Capitol, explaining why she might be willing to support the current measure despite voting against the last one. “Nobody knew what we were really . . . voting on.”

Republicans, who hold 52 seats in the Senate, are already contemplating a scenario in which they are unable to persuade Sens. Rand Paul (R-Ky.) and Susan Collins (R-Maine) to back their effort. That leaves them with no defections to spare even with Vice President Pence available to cast a tiebreaking vote on a bill that Democrats uniformly oppose.

And it makes Murkowski the GOP’s biggest remaining challenge, Republicans familiar with the situation said this week.

The senator from Alaska has offered few clues as to where she stands in the negotiations. She met at length this week in McConnell’s office near the Senate chamber, and she has remained in close contact with Cassidy and his team as she seeks to better understand what the bill means for Alaska.

Murkowski and her team insisted that she is interested in seeing more numbers crunched to make a responsible decision. But some Republicans with a close eye on the process are under the impression that she is more interested in gaining political cover.

Beyond that, it has become a Capitol Hill parlor game to guess what could move her and whether it would work without prompting an avalanche of similar demands from other senators.

“If it can be shown that Alaska is not going to be disadvantaged, you gain additional flexibility,” Murkowski said. “Then I can go back to Alaskans, and I can say, ‘Okay, let’s walk through this together.’ ”

Comparing it to the July effort, she added: “That’s where it could be different.”

Murkowski is the daughter of Frank Murkowski, a fixture in Alaska politics for three decades who appointed her to his Senate seat in 2002 when he became governor. Since that time, she has forged her own identity as a centrist Republican and the chairman of the Senate Energy and Natural Resources Committee. But she has also followed a succession of politicians, including her father and the late Ted Stevens, known for engaging in political horse-trading to bring resources home to Alaska.

She has also demonstrated a regular willingness to buck her party. In 2010, she defied the odds when she lost the Republican primary to a tea party challenger only to come back, with little institutional support, and win the general election as a write-in candidate.

Now, President Trump and McConnell (R-Ky.) have a second chance to keep Murkowski in the fold after their heavy-handed efforts to sway her in July appeared to backfire.

In the lead-up to the July vote, Trump took to Twitter to call out Murkowski for not being more supportive. He also placed a call that she described as unpleasant and dispatched Interior Department Secretary Ryan Zinke to make what some interpreted as a threat that federal resources for Alaska could be at risk if she voted no.

At the time, Murkowski also complained about McConnell’s secretive method of crafting a bill with a small clutch of aides and away from most Republican senators, including her.

This time, there are signs that Trump and McConnell are doing things differently.

Murkowski has been spared public displays of aggression from Trump — and some GOP Senate aides are keeping their fingers crossed that it will continue. The president lashed out at Paul on Twitter, calling him a “negative force” on health care. In New York at a meeting with the president of Egypt, Trump praised the Cassidy-Graham bill and told reporters he believed “47 or 48” senators supported it and “a lot of others are looking at it very positively.”

Pence and White House legislative director Marc Short have conducted much of the outreach to on-the-fence senators this week, revealing little public information about whom they are contacting or what they are saying.

Asked Monday whether the president could persuade her to vote for the latest repeal-and-replace bill, Murkowski responded: “If he has the numbers, yeah.”

Murkowski’s fierce advocacy on health care springs largely from a unique set of factors in Alaska: a poor and vulnerable population, remote geography and inordinately high health-care costs. Alaska is one of a handful of Republican-controlled states that expanded Medicaid under the Affordable Care Act — meaning that the current bill’s proposed cuts and redistribution of federal health-care dollars could strip thousands of Alaskans of coverage. At the moment, the legislation would turn funding for the ACA into block grants for states and, over time, sharply slash Medicaid spending.

The state’s governor, Bill Walker (I), opposes the Cassidy-Graham bill, as do other Republican governors. Nevertheless, McConnell is moving forward to try to take advantage of a procedural window to pass the bill with 51 votes that will close at the end of the month.

“It is the leader’s intention to consider Graham-Cassidy on the floor next week,” his spokesman, Don Stewart, said Wednesday.

But not everyone is eager to plow ahead. Sen. Charles E. Grassley (R-Iowa) expressed doubts Wednesday that the bill would pass, according to the Des Moines Register.

Speaking Wednesday at an event hosted by the Bill & Melinda Gates Foundation, former president Barack Obama said that any effort to repeal the ACA would end up “inflicting real human suffering” on Americans who had gained health coverage and consumer protections under his signature law.

Throughout the week, Murkowski has sought to keep comments laser-focused on her state. On her way to McConnell’s office this week, reporters informed Murkowski that the nonpartisan Congressional Budget Office had just announced it would not release information on how the bill would impact premiums or projected changes to the number of people with insurance coverage “for at least several weeks.”

“Oh, why?” she asked.

A reporter read from the CBO’s news release.

“Hmm,” Murkowski responded. Asked whether she could vote for a bill without that information, she dodged: “What I’m trying to figure out is the impact on my state.”

Top Republicans have speculated that providing further protections for Alaska from the Medicaid cuts is one solution — although that could set off a string of demands from other senators. Others have suggested stripping out or amending a one-year Medicaid funding freeze that the legislation would impose on Planned Parenthood, given Murkowski’s support for the organization. That, however, could upset socially conservative senators.

Collins could also influence Murkowski in the other direction. They both voted “no” on the last effort, and have become allies over the years. So could Sen. John McCain (Ariz.), the third Republican to vote no in July and another undecided senator this time.

Collins has been very outspoken about her concerns with the latest legislation. McCain’s home state governor, Republican Doug Ducey, has come out in support of the bill. That, coupled with McCain’s close relationship with Graham, has led some Republicans to conclude that he is a gettable vote.

As for Murkowski, it’s wait and see.

“I am doing the due diligence that I committed to doing,” she said Wednesday.

Juliet Eilperin, Mike DeBonis, Abby Phillip and Kelsey Snell contributed to this report.