At the moment, however, it appears Biden plays the game better:

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.

Tanden’s withdrawal reportedly surprised Murkowski, in part because Tanden wasn’t her focus at this moment. She’s a lot more concerned about Haaland at Interior, where regulatory and policy decisions will have a lot more impact on her constituents. “They know who the secretary of the Interior is,” Murkowski told the Post’s reporters, but “they’ve never heard of the OMB.” Biden has already issued EOs that negatively impact Alaska, and Murkowski wants to make as much of an effort to push back — but might be stuck with Haaland no matter what:

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.

This is actually not much different than the position in which Manchin finds himself. West Virginia’s economy runs on coal and other fossil fuels, which Haaland will no doubt target as Interior Secretary. On the other hand, the policy is coming from the White House more than it comes from Haaland. That reality is likely why Manchin threw in with Haaland last week. That reduces Murkowski’s leverage on Haaland, and so does the endorsement of Alaska’s Republican Rep. Don Young. With every Democrat expected to support Haaland, and now Susan Collins also backing her, Biden doesn’t really need Murkowski.

That might be why Murkowski got surprised by Tanden’s withdrawal. Haaland might have been Murkowski’s focus, but Tanden was likely her best leverage. Now that Tanden has withdrawn and Collins has crossed the aisle on Haaland, it leaves only two possibilities. One: Murkowski just got outboxed by Biden. Two: Murkowski got what she wanted from Biden on aid to Alaska and let Tanden withdraw to save face. I’m guessing it’s the former, but both are possible.

If Biden outplayed Murkowski, it comes at a very bad time for the Alaska incumbent. Donald Trump is threatening to spend big-league to unseat her in 2022, and the economic impact of the COVID-19 pandemic — especially on tourism — might destabilize the politics of the state. Murkowski needs some big wins in this session, and with Democrats in charge, that means Murkowski needs Biden more than Biden needs Murkowski. That makes Biden the Monty Hall in this relationship … and Murkowski a very brittle ally for Mitch McConnell in this session.