But the adjustments proposed Tuesday don't yet appear to be enough to yield the 21 votes needed for the legislation to pass the 40-member House, with two moderate Republicans, Reps. Paul Seaton of Homer and Louise Stutes of Kodiak, quickly voicing skepticism.
"If the proposals that we've had thus far don't get them to 21, there's not enough of a change going on in these last two versions to materially change how people feel about it," Brad Keithley, an oil and gas consultant and budget hawk, said in a phone interview. "Unless somebody just wants to change their vote."
The new proposal from Johnson, unveiled at a Tuesday hearing of the House Rules Committee he chairs, is the first public action on HB 247 since it faltered on the House floor April 13 and was returned to the committee for surgery.
Since then, lawmakers have made essentially no public progress on any of Gov. Bill Walker's proposals to reduce the state's $4 billion budget deficit — from tax increases to oil tax reforms to his plan to restructure the Permanent Fund to generate revenue for state government.
House and Senate leaders say the oil tax impasse must be resolved before they can do substantive work on other bills, since the amount of state oil revenue — and the amount of cash subsidies paid to small oil companies — will determine how much of a gap remains for other legislation to fill.
Johnson, in a phone interview after Tuesday's hearing, described the latest version of HB 247 as a compromise that few people would like — but one he hopes that his colleagues can accept.
"I don't know anyone that loves this bill," Johnson said. "The producers don't like it. The governor doesn't like it. Paul Seaton and his group don't like it. I don't like it. Maybe it's the right bill."
He added, "It's time to fish or cut bait."
Johnson said he hopes HB 247 can move out of his committee in a day or two, after votes on amendments, then pass the House by the weekend to give the Senate enough time to work on it.
Lawmakers are now in their fourth week of overtime after the end of their 90-day scheduled session, and they're nearing a 121-day constitutional limit, which comes next week.
The session can be extended for up to 10 days beyond that, but doing so requires a two-thirds vote of the House and Senate.
If Johnson's proposal fails, lawmakers will likely end up debating a new oil tax bill proposed by Walker during a special session, Johnson said.
The new legislation and Tuesday hearing by Johnson's committee appeared to set back a parallel compromise effort that Seaton and Rep. Tammie Wilson, R-North Pole, were working on last week.
The two lawmakers are at polar opposite ends of the House majority's caucus' ideological split, which has been one of the primary hurdles in assembling the 21 votes needed to pass an oil tax bill to the Senate.
Members are trying to reduce cash subsidies that the state pays to small oil and gas companies, projected at $775 million next year, and to maximize the state's flow of oil revenue in a way that doesn't drive companies and investors away from Alaska.
Democrats and moderate Republicans like Seaton favor sharper cuts to the subsidies, as well as changes to the oil tax system to limit companies' ability to keep credits or deductions that they can't apply against taxes in the current year. By the end of the 2018 fiscal year, the Walker administration projects those "carried-forward" credits to be $750 million — which companies will ultimately deduct from their taxes at some point in the future.
Wilson and the majority's leadership, which includes Johnson, favor more gradual reductions to the cash subsidies, as well as keeping the system that allows companies to preserve their credits or deductions for more than one year.
Wilson claimed last week that a set of ideas she and Seaton had agreed on — including a gradual elimination of the carried-forward credits — had 20 supporters, just one vote shy of the number needed to pass.
Seaton said in a phone interview Tuesday that amendments to convert a prior version of the legislation to his compromise measure had already been drafted.
Now, he added, "we have to re-craft everything to this rules version, it appears."
"Our goal was limiting the state's liability -- I'm uncomfortable with the amount of liability that's been limited here," Seaton added, referring to Johnson's new proposal.
Johnson's legislation does make some concessions aimed at picking up moderate votes.
Among them: It caps at $75 million the cash subsidies that can be collected by a company in a single year, which is down from $85 million in a previous proposal from Johnson's committee.
It also ramps down cash subsidies to Cook Inlet oil and gas companies more quickly than previously proposed — though not as quickly as Seaton and Wilson would like.
And it tweaks the tax system for big oil companies on the North Slope, forcing them by 2020 to pay a full 4 percent minimum tax that, under the current system, can be reduced using credits generated when companies lose money. The Walker administration estimates that that change could ultimately generate as much as $100 million in extra annual revenue for the state.
But the legislation also preserves two key components of the current system that have been criticized by Democrats and moderate Republicans.
One is the 35 percent rate at which companies accrue credits or deductions based on their losses. The other is the ability of those companies to carry forward those credits or deductions into future years.
Stutes, the Kodiak Republican, said in a phone interview that the preservation of the 35 percent rate is "an issue" for her — though she stressed that she was still unfamiliar with the details of the legislation.
"If everybody's going to get cut, the oil companies are right in there too," Stutes said in a phone interview. "And they need to feel their share of pain as well."
Another potential problem as the oil tax legislation advances is the position of the House Democratic minority.
The Republican-led majority doesn't need minority votes to pass HB 247. But it almost certainly will need them to fund the state's budget — which will likely rely on money from a state savings account that requires a three-fourths vote to access. Democrats are likely to tie those votes to an oil tax package that's acceptable to them.
Anchorage Democratic Rep. Andy Josephson, one minority member who's worked on oil taxes, said the only path forward he sees for Johnson's legislation — known as a committee substitute bill, or CS — is one in which it's amended to look more like the compromise from Seaton and Wilson.
"I can't imagine a single member of my caucus would vote for the CS that came out today," Josephson said.