Alaska also could see further hits to its credit rating, which has already been downgraded. The governor has warned that legislators could face a special session if they do not come up with a fiscal plan before the regular session ends on April 17.

The Senate president, Kevin Meyer, a Republican, said he believes legislators have the right attitude — “that we need to do something and we need to do something major.” What that ends up being remains unclear.

Among the big pieces in play: Bills that would allow for structured annual draws from the earnings of the Alaska Permanent Fund to help pay for state government. Changes to the Medicaid and oil and gas tax credit programs, which have become major budget items. Bills to reinstitute a personal state income tax for the first time since 1980 and proposals from Mr. Walker to raise taxes on motor fuels and on various industries, including oil, fishing and mining. State spending plans also need to be completed.

The major debate at this point appears to be around using earnings from the Alaska Permanent Fund, what tax bills to pass, if any, and how far to push changes to oil taxes and credits. There is debate, too, over how much needs to be done this year.

Some legislators still see room to cut the budget and do not want to create or raise taxes at this point. Others say everything needs to be discussed, even adding triggers to tax bills that would revoke any increases if oil prices hit a certain level.