JUNEAU — The prospect of a special session loomed as Alaska lawmakers hit their fourth month in regular session without agreement on a plan for pulling the state out of a massive budget deficit.

Lawmakers worked past the voter-approved 90-day session limit in April after failing to come to terms on changes to Alaska’s oil and gas tax credit system. The state constitution allows for 121-day regular sessions, a mark lawmakers will reach Wednesday.

They have the option of extending for up to 10 days but need a two-thirds vote on each side to do so. Gov. Bill Walker, who has said he wants a complete fiscal plan passed this year, also could call them into a special session, which some legislative leaders expect.

House Speaker Mike Chenault said he would like to be able to get a budget passed before going into any special session to put state workers’ minds at ease. Last year, state employees received layoff notices as a legislative dispute over the budget spilled into June. The new fiscal year begins July 1.

“I know we’re not going to get to all the revenue measures, but the governor is going to call us back on those anyway,” Chenault, R-Nikiski, said in an interview Monday.

Senate President Kevin Meyer, R-Anchorage, on Tuesday said he would like to see the budgets and oil tax credit bill passed by Wednesday but said that may be overly optimistic. “It’s all pretty much contingent on the House now,” he said.

House Minority Leader Chris Tuck said his caucus doesn’t want to give up the leverage it has for funding the budget without knowing what the overall fiscal plan will be. Generally, a three-quarter vote is needed in each the House and Senate to access the constitutional budget reserve to help cover costs. That’s not a problem in the Senate, where 16 of its 20 members belong to the Republican-led majority. Reaching that threshold in the House, though, requires support from the Democratic-led minority.

Should a three-quarter vote fail, an option that’s been raised is using earnings from the Alaska Permanent Fund to cover budget costs. A three-quarter vote is not necessary to access the fund. Walker spokeswoman Katie Marquette said it was too soon to say if the governor would veto a budget funded with permanent fund earnings.

“Our issues are immediate and unavoidable, and so I must insist that we keep working together for as long as it takes to solve them,” Walker wrote in a letter to lawmakers dated Saturday.

Tuck, D-Anchorage, said he would rather go into a special session than further extend the regular session, to limit the issues under consideration.

Work by lawmakers Tuesday included the Senate Finance Committee advancing an oil and gas tax credit rewrite that takes a different approach than what passed the House with Democratic buy-in last week. Tuck called that rewrite “bogus.”