JUNEAU — An Alaska legislative committee on Tuesday unveiled a draft oil and gas tax credit bill aimed at breaking an impasse that helped send lawmakers into overtime, proposing to phase out most existing credits and calling for a new tax structure for Cook Inlet by 2019.

But it received a muted response from some lawmakers who say it doesn’t go far enough in making changes or lowering the state’s tax liability. The head of the Alaska Oil and Gas Association, meanwhile, said the draft, like previous versions of the bill, would hurt the industry.

Legislative leaders see reaching agreement on tax credits as crucial to making further progress on the budget and revenue bills, including the proposed use of Alaska Permanent Fund earnings to help pay for state government. Alaska faces an estimated $4 billion budget deficit exacerbated by low oil prices.

Lawmakers face a looming constitutional deadline to complete their work or could wind up in special session. Under the constitution, regular sessions can last up to 121 days, a mark that will be reached next week. The constitution allows for an extension of up to 10 days.

“We’re sort of at the point now where we have to make some decisions,” said Rep. Craig Johnson, R-Anchorage, and chairman of the House Rules Committee, which released the draft.

The committee inherited the bill after it appeared that a previous iteration would fail if brought to a vote on the House floor. Tuesday’s meeting was notable since it followed weeks of fits and starts where meeting notices acted as mere placeholders and lawmakers informally tried to see if there were areas they could rally around.

Johnson called the draft a melding of different ideas and a starting point to “move forward with some kind of system that allows the state to generate additional revenue while maintaining the opportunity for our partners to continue to do business.”

According to a summary of the bill, the draft, among other things, would phase out existing credits in the state by 2020, except for credits for an area south of the North Slope and outside of Cook Inlet, known as “middle earth,” set to expire in 2022. The phase-out of Cook Inlet credits would coincide with the implementation of a yet-to-be-determined tax structure for Cook Inlet starting in 2019.

The draft would limit what is now a timeless tax break for oil from newer North Slope fields to 10 years, a longer duration than proposed by other versions of the bill, and change net operating loss credits that major North Slope producers currently could use to offset their tax liability into lease expenditure deductions that can be carried forward.

Rep. Paul Seaton, R-Homer, said the rewrite falls short of several goals he had, including lowering the state’s liability, having as big an immediate budget impact as possible and protecting smaller players.

House Minority Leader Chris Tuck, D-Anchorage, said he also has concerns with the rewrite. Meaningful changes to the credit structure are needed to show Alaskans that lawmakers are serious about fixing the state’s fiscal situation, he said.

Kara Moriarty, president and CEO of the Alaska Oil and Gas Association, said the result from the kinds of changes being contemplated to the credit structure will be less production.

She said her group views the draft rewrite as a “short-term grab for the state that will have significant consequences on the long-term revenues for Alaska.”