The display cases at Paul’s Cigars, in the North Portland enclave of Hayden Island, offer an impressive array. Dozens of varieties of stogies sit in ornate boxes, their pungent potential locked away behind glass.

Owner John Paul has spent years amassing this inventory. And lately as he’s surveyed his collection, he’s begun doing a quiet math:

“This $10 cigar will be going to $13.50,” said Paul, pointing out products on a recent tour around his store. “That one’s gonna go up $3 a stick. This one will go up about $4 and a quarter a stick.”

Like other neighboring businesses, Paul’s Cigars is preparing for what many on the island believe is inevitable. Oregon leaders are looking for nearly $1 billion to pay for the state Medicaid program, the Oregon Health Plan. And one key proposal from Gov. Kate Brown is a big increase in tobacco taxes.

A bill before the Oregon Legislature would hike taxes on cigarettes by $2 per pack. That would raise Oregon’s tax to $3.33, bringing it essentially even with cigarette taxes in California and Washington.

Brown also wants to tax vaping products and eliminate a 50 cent cap on taxes for large cigars that Paul says will make them far more expensive.

The proposal would be felt around Oregon, but could have a special effect on Hayden Island, long a magnet for cost-conscious Washington state smokers looking for cheap smokes.

“I have stores in Washington and Oregon, so I’m covered either way,” Paul said. “But Oregon will lose a lot of sales to Washington.”

That doesn’t worry Patrick Allen, the director of the Oregon Health Authority.

His agency oversees health care for nearly 1 million low-income Oregonians. For the last two budgets, he’s faced daunting gaps in the state’s ability to pay for that coverage.

Allen and his boss, the governor, hope this is the last time they need to have a funding fight — at least for a while. The plan they’re pushing would fund the Oregon Health Plan for the upcoming six years, avoiding an every-other-year scramble for money or worries over cuts to coverage.

Lawmakers already filled a big part of a $922 million funding gap in the upcoming budget by passing House Bill 2010. The $380 million package implemented a series of taxes on hospitals and health insurers.

Brown’s office is also pushing a new tax on employers who don’t offer their employees health coverage, which could account for roughly $60 million a year.

But the tobacco tax hike is expected to bring in far more — around $175 million a year. And while the money likely isn’t necessary to fund the Medicaid system in the short term, it’s a central part of the plan to stabilize health care funding on a longer timeline.

“It is very difficult to sustain funding for the Oregon Health Plan for more than a two-year cycle without that cigarette tax,” Brown said.

Allen argues there’s far more to the idea than money. In fact, he says the OHA first began working on the proposal without taking new revenue into account.

“We thought a $2 increase to put us on relative par with Washington and California was the right thing to help adults quit smoking, stop kids from starting smoking, reduce the amount of money spent on health care due to tobacco,” Allen said. “Honestly, from our standpoint as an agency, that was the real driver.”

Allen says there’s no good argument against raising tobacco taxes. But that doesn’t mean Oregonians won’t hear plenty if this idea moves forward.

In 2007, voters overwhelmingly shot down a ballot measure that would have raised taxes by 85 cents per pack. The proposal was hammered by the tobacco industry, which spent $12 million to defeat it, compared to less than $4 million raised by proponents.

State Sen. Laurie Monnes Anderson, D-Gresham, was a central champion of the ballot measure. She says it was doomed by the lack of funding and the fact that it would have amended Oregon’s constitution.

“[Opponents] said, ‘How can you want to change the constitution? The Legislature’s trying to change the constitution,’” Monnes Anderson recalled recently. “They made a big deal about it.”

Six years later, in 2013, lawmakers raised cigarette taxes by 13 cents a pack as part of a “grand bargain” bill struck under then-Gov. John Kitzhaber. Under the bill, the increase eventually ticked up to 15 cents a pack.

This year, Brown wants to go much further. But to pass a tax without putting it to voters she’ll need support from three-fifths of lawmakers in the House and Senate. She said recently she feels “really good” about the chances of doing that, but conceded she’s not sure if the votes exist.

“I haven’t done a specific vote count,” Brown said. “I will just say the need is great and growing more obvious every day.”

House Speaker Tina Kotek, D-Portland, also hasn’t polled her members on the tobacco tax, though she noted, “We have a lot of people who really believe we need to do it this session.”

Monnes Anderson worries that that urgency could get lost in the shuffle as lawmakers consider a slate of ambitious bills this session, including one that’s expected to raise $1 billion a year for schools.

“Probably the cigarette tax is the second priority, and there are only so many taxes that people will vote for,” she said. “It’s so fragile at the end of session with so many bills.”

Given that sensitivity, Monnes Anderson thinks lawmakers may vote to send the tax to voters rather than passing it outright.

“We could have run a better campaign [in 2007], and we will if we do it again,” she said. “I hear that the insurance carriers will be behind it. The hospitals will be behind it. Providers will be behind it. So we will have a much bigger coalition.”

Not far from the cigar shop on Hayden Island, Karen Bailey works the counter at a combination bar, deli and video lottery parlor. But Bailey says at least 60% of her customers stop in just to buy cigarettes.

And like Paul, at the cigar shop, Bailey’s business has been preparing for a big change.

“I’ve been telling the Washington people we’re going to be raising two bucks a pack,” she said on a recent morning. “I’ve been getting a lot of, ‘Uh, maybe time to quit.’”

The tax hike wouldn’t break the deli, Bailey says. Cigarettes aren’t where the real money is. Plus, she’s been expecting prices to increase for a long time.

“Washington, Oregon, California kind of go hand-in-hand,” she said. “Whatever one does then somebody catches up. Doesn’t matter which one goes first.”