JUNEAU — Alaska legislators face a looming constitutional deadline for completing their work, but they remain at odds over how best to address a multibillion-dollar state budget deficit.

Lawmakers have been grappling with that issue since failing to come up with a long-term solution last year. The state, which has long relied on oil revenue, has been using savings to help cover expenses amid chronically low oil prices.

While there’s general agreement about using earnings from the state’s oil-wealth fund — the Alaska Permanent Fund — as part of a fiscal plan, there are sharp differences over what else should be done.

The House majority, composed largely of Democrats, has seen a broad-based tax like an income tax as a key piece for a fiscal plan and has been supported in that position by Gov. Bill Walker, a Republican turned independent. The House majority made its support of the use of permanent fund earnings contingent upon passage of a broad-based tax and a rewrite of oil tax and credit policy, seeing that as a more balanced approach.

The Senate last week made official its long-standing opposition to an income tax by voting down the tax bill that passed the House. Its approach on oil taxes and credits also differs from the House.

The Republican-led Senate has proposed limits on future spending and cuts to public education and the university system that the House majority considers too deep.

The budget impasse, too, remains unresolved.

Senate President Pete Kelly told reporters Friday that compromising is not the goal. “Doing what’s in the best interest of the state of Alaska is the goal,” the Fairbanks Republican said.

House Finance Committee co-chair Rep. Paul Seaton said a solution that relies on permanent fund earnings alone is not enough. In terms of a path forward, “It’s difficult to try and figure out where we’re going to go,” said Seaton, one of three Republicans in the House majority coalition.

House Speaker Bryce Edgmon said Friday that he thinks there might be room for negotiation on other revenue options, but he did not say what those might be.

The constitution allows for regular sessions of up to 121 days, a mark that will be reached on Wednesday.

The Legislature can extend itself another 10 days with two-thirds support in each chamber. Another option is a special session.