As early as December, the incoming Biden administration began to woo a Republican who could prove pivotal in their legislative efforts: Sen. Lisa Murkowski of Alaska.

As transition officials sifted through an assortment of potential Cabinet picks, they would run lists of names by the veteran senator for her feedback: Does Murkowski know any of these people? How do you feel about them? Could they survive a difficult confirmation process?

At a time when senior Democrats weren’t getting advance notice on key Cabinet picks and control of the Senate was up in the air, Murkowski had already held numerous conversations with transition aides — a sign of her influence, no matter which party would be in power.

“I don’t know what they’re doing with my advice,” Murkowski said at the time, chuckling. “They may be listening politely and saying, ‘Well, that was nice’ and doing something else. But at least you know that you have an opportunity to just weigh in and say, ‘That would be a really bad choice.’ ”

Nearly three months later, Murkowski is at the nexus of several of President Biden’s immediate and longer-term priorities on Capitol Hill, approaching each fight with a fiercely independent streak that could prove mutually beneficial for both her and the White House as she faces reelection next year.

She kept political Washington guessing for a week on whether she would step in and save the nomination of Neera Tanden as the administration’s Office of Management and Budget chief, engaging in lengthy conversations with the White House and Tanden until the nominee withdrew herself from consideration on Tuesday. She is also being closely watched on the nomination of Rep. Deb Haaland (D-N.M.) for Interior secretary, who faces a committee vote Thursday morning.

And Murkowski made it clear in interviews Wednesday that her vote on Biden’s coronavirus relief package is up for grabs — at a time when Senate Republican leaders are trying to coalesce unified GOP opposition to the massive $1.9 trillion bill. The White House is desperately seeking Murkowski’s support, which would give the president’s top legislative priority some bipartisan veneer.

“My state needs relief,” Murkowski said. “If Congress is going to move this much money out the door, how am I going to make sure that states like Alaska — who have been significantly impacted, who are still in need of rescue, if that’s the term that they’re using for this package — that we, in fact, get those, get access to those rescue dollars?”

A Biden official close the process, who spoke on the condition of anonymity to discuss a private conversation, said Tanden and Murkowski “had a good conversation, which was appreciated. The president is serious about working across the aisle and having a constructive working relationship.”

Murkowski has maintained that she never requested any concession from the White House in exchange for backing Tanden or any other nominee. But Republican allies see this entire effort — haggling over Tanden, weighing the Haaland nomination and considering supporting the rescue package — as a maneuver on Murkowski’s part to deliver as much as possible for her state without alienating too many supporters.

A vote against Haaland could lead her to support the coronavirus relief bill if Democrats are willing to accommodate Murkowski to deliver for the native community, according to these Republicans, who spoke on the condition of anonymity to candidly discuss the senator’s thinking. A vote for Haaland could suggest that she will stand against the relief package.

Murkowski said her state has suffered disproportionately due to the coronavirus pandemic, particularly as Alaska saw a steep revenue decline with a relatively smaller population. Formulas in the relief package that outline how much aid each state receives does not account for the outsized fiscal pain that is confronting her state, she said.

The pandemic caused job losses in Alaska at a rate not seen in decades, with a third of the more than 27,000 lost jobs coming from the leisure and hospitality industry, according to the Alaska Department of Labor and Workforce Development.

“If you’re a community like Skagway, Alaska, that has suffered a 90 percent revenue loss from last year because there’s no tourism, because the cruise ships didn’t come last year and they’re not going to come this year?” Murkowski said of the pending relief bill. “They’re going to look and say, ‘Well, you get to spend a lot of money. But how did how did it help a community like ours?’ ”

The pandemic-induced economic struggles are persisting at a time when the Alaska oil sector has been the target of executive actions from the Biden administration, such as one that temporarily halted oil- and natural gas-leasing activities in the Arctic National Wildlife Refuge on his first day in office.

So Murkowski said she is taking every opportunity — whether it’s sit-downs with nominees who need her support, or conversations with White House officials about the coronavirus relief package — to press Alaska issues, noting that economic projects in her state have been the target of more than a half-dozen executive orders during the early weeks of the Biden administration.

“I’m using this getting-to-know-you time by educating everyone that I’m coming into contact with about Alaska-specific needs,” she said.

In doing so, Murkowski — who began serving in the Senate in 2002 — is drawing on years of experience securing benefits for her state, such as a provision in the sweeping GOP tax overhaul in 2017 that opened up drilling in parts of the 19 million-acre wildlife refuge.

She also helped thwart the Republican Party’s attempts to repeal the Affordable Care Act in 2017 and voted against controversial nominees under the previous administration such as former education secretary Betsy DeVos. She opposed the confirmation of Supreme Court Justice Brett M. Kavanaugh and wanted to block the nomination of Justice Amy Coney Barrett from advancing, although Murkowski ultimately supported Barrett on her merits.

“She’s very well-liked but she’s a strong, independent person,” said one senior Republican aide, who spoke on the condition of anonymity to speak frankly. “She definitely does her own thing at times.”

For all of Washington’s infatuation with the Tanden tale of the last few weeks, Murkowski said her constituents remain far more interested in where she will land Thursday when the Energy Committee will vote to advance Haaland’s nomination to the full Senate.

“They know who the secretary of the Interior is,” she said of Alaskans. “They’ve never heard of the OMB.”

Murkowski said she expects to reveal her decision on Haaland before the committee meets, but acknowledged that she is certain to alienate key allies no matter her decision.

On one side is the state’s energy sector, which is the dominant industry for a state that relies heavily on oil drilling for employment and revenue. Energy officials there oppose Haaland’s liberal positions on their industry and are furious with the early executive orders.

On the other side are Alaska Natives, who make up nearly 20 percent of the state’s population and have been closely allied with Murkowski for decades. Their support has been crucial to her past election victories, and they are pushing Murkowski heavily to vote for Haaland as the first Native American to lead a department so critical to the state.

The in-state dynamics are unfolding at a time when Murkowski is campaigning for her fourth full term and when former president Donald Trump is vowing publicly and privately to work to oust her. Of the seven GOP senators who voted to convict Trump in his impeachment trial, Murkowski is the only one who is running for reelection this congressional cycle.

A Trump-backed primary challenge against Murkowski is by no means certain at this point, as advisers to the former president recognize the complexity of winning in Alaska, which recently adopted ranked-choice voting and a nonpartisan top-four primary system. Murkowski won reelection in 2010 as a write-in candidate after losing the GOP primary.

During a speech Sunday at the Conservative Political Action Conference, Trump included Murkowski in a long list of “grandstanders” who he said the party had to “get rid of,” after they criticized him or voted to support his impeachment.

Murkowski is higher on his list of enemies than other senators and lawmakers. One adviser, who spoke on the condition of anonymity to describe private conversations, recently said Rep. Liz Cheney (R-Wyo.) topped Trump’s list, then came Murkowski and then Georgia Gov. Brian Kemp (R). Trump does want to spend money against her, this adviser said.

Some people in his circle doubt, though, that he will be as much of a potent force in the race because traveling to campaign against her would require such a long flight, which Trump generally avoids.

Nonetheless, the sheer number of conservative efforts to raise funds for Republican challenges make it likely that Murkowski faces some opposition from the party’s pro-Trump base.

“The biggest problem isn’t necessarily Donald Trump. It’s the grass roots,” said one person in Trump’s circle, who spoke on the condition of anonymity to describe private conversations. “Every other person you talked to at CPAC tells you they have a super PAC.”

Michael Scherer, Josh Dawsey and Tyler Pager contributed to this report.