Washington (CNN) When Republican Sen. Lisa Murkowski helped defeat her own party's bill to repeal Obamacare earlier this year, she said she was applauded upon her arrival at airports across her home state of Alaska.

Now that Republicans have added a plan to roll back a significant part of Obamacare to their tax bill , attention has once again shifted to the three-term senator. Republicans can once again only lose three senators or their efforts will fail, but GOP leaders are optimistic that Murkowski will side with her party this time.

That's because the tax plan, due to arcane Senate rules, will be combined with a bill that would open up Alaska's Arctic National Wildlife Refuge, or ANWR, to oil and gas drilling.

Drilling in ANWR is an issue that's long been near to Murkowski, in part because her father, Frank Murkowski, a former Republican senator and governor, also advocated for drilling but was unsuccessful.

Proponents of opening up ANWR say it would significantly help Alaska's economy, and adding it to tax reform will help give the package more revenue to pay for tax cuts. Opponents argue that drilling there would be harmful to fish and wildlife in Alaska's Coastal Plain.

Murkowski said Thursday that she worries about bringing the individual mandate into the tax reform debate.

"Both pieces of those are complicated and together they become more complicated," she said.

But Murkowski realizes that if she votes against the tax bill, she'd be voting against opening up ANWR -- "which would not be something that I would want."

So why is ANWR tied to tax reform?

Republicans are attempting to pass tax reform using budget reconciliation, a procedure that allows them to advance a bill with only 50 votes. Since Republicans have a 52-48 majority in the Senate, this means they could pass legislation without any Democratic votes.

But to use reconciliation, the legislation must adhere to instructions written by the Senate Budget Committee designed to keep deficits in check over the next decade. Part of the instructions for tax reform included directions to the Senate Energy and Natural Resources Committee, which Murkowski chairs (as did her father), to come up with $1 billion in deficit reduction.

That was essentially a greenlight for Murkowski and her committee to pass her ANWR drilling bill, which would raise revenues to help pay for tax cuts.

Republicans can only afford to lose two Republicans to pass their tax reform package, so Murkowski's vote will be critical.

"I am certainly trying to be helpful and constructive, although, as you know, I've been focused on the energy committee's piece and how that all fits in," she said Thursday, adding that she's "looking very, very carefully at what the finance committee is doing" on the tax bill.