Gov. Paul LePage is still eyeing ways to accomplish his long-stated goal of eliminating Maine’s income tax.

Rather than try to sway a wary Legislature, the governor is looking at a referendum question that would let voters decide whether to do away with “this unruly income tax.”

LePage told Portland radio station WGAN Thursday that legislators are increasingly out of the loop, given the state’s growing reliance on ballot questions that put the decision in the hands of voters instead.

“The Legislature’s relatively irrelevant,” the two-term governor said.

Hold a referendum, LePage said, and legislators will go along with the results, saying, “Well, the people have spoken.”

“And that’s how you win the game,” the governor said.

Getting rid of the income tax has always been a LePage goal.

As he put it in his 2015 State of the State speech, “My vision for Maine is a Maine without an income tax.”

But when the state Republican Party tried to gather the 61,000 signatures needed to put the idea on the ballot this year, it gave up after it couldn’t collect enough names to make the cut. The GOP said then that it might try again in 2017.

Abolishing the tax would slice away nearly half the $3 billion in annual revenue needed to fill state government coffers.

But LePage argues the state would be better off if it raised the sales tax to make up the gap.

The budget proposal the governor is required to deliver Friday likely won’t call for elimination of the income tax, but LePage said he’ll seek to lower the 7.1 percent rate now in place.

For top earners, he’s expected to seek a rate low enough that the 3 percent hike imposed in a November referendum question approved by voters won’t actually cause high earners to pay anything more. The ballot question sought extra money for education from households reporting more than $200,000 in yearly income.

LePage said the state can’t sustain an effective tax rate of more than 10 percent, but he is not yet sure how much he can lower it.

LePage said the income tax rate ought to be zero, with the sales tax raised and broadened in scope to raise additional revenue.

He said that because “people love to come to Maine” in the summer for its ideal climate and beauty, it makes sense to try to get them to pay more sales taxes during their vacations rather than hitting up Mainers who generally have less money to begin with.

The governor said he’s looking at ballot questions to get what he wants because legislators always want to “play politics” rather than work with him to create good policy for the state.

He said, for example, he is planning to propose an initiative to have the state cover the cost of paying teachers across Maine and leave it in the hands of local school officials to handle how much they want for other educational costs, such as administrators.

“I’ll take care of the classroom operations,” LePage said, and have the state cover between 50 and 55 percent of the overall tab for schools.

LePage said the move will save $400 million, but he doubts lawmakers will go for it because “the unions run the state” and Democrats won’t buck them.

The governor said he’ll talk about the idea at a new round of town hall meetings he plans to begin next week. The location of the first one is not yet known.

LePage said that he had success pushing welfare reform by talking about it with voters, eventually winning over so many of them that the Legislature had to go along.

“That’s my new approach. I’m going directly to the Maine people,” the governor said.

During his radio interview, LePage also said two companies with 400 jobs between them are planning to shut down in Maine because of high costs, especially for energy. But he didn’t provide any details.

If the governor is successful in getting his income tax proposal on the ballot, it won’t be the first time Mainers have had a chance to vote on the issue.

The income tax issue has faced voters at least three times in the past.

The first time, in 1920, voters gunned down a proposed state constitutional amendment to allow for an income tax by a 60-40 margin. In 1949, they again turned it down.

But when it came up again in 1971, three-quarters of Mainers endorsed the tax, which has remained on the books since.