SEATTLE — An initiative seeking to repeal Washington's new income tax on $1 million-plus earners trails badly in a new poll when voters are shown legally required ballot language summarizing its potential impacts on the state budget.

The statewide poll by Portland, Oregon-based polling firm DHM Research tested support for Initiative 645 with and without the fiscal-impact language, which states the measure's passage would decrease funding" for public K-12 schools, universities and healthcare.

The poll of 800 Washington residents tested support for I-645 by evenly splitting the sample: 400 saw that budget-impact wording, and 400 did not.

It made a big difference.

Fifty-seven percent of those who saw the budget statement said they'd vote no on I-645, compared with 35% who said they'd vote yes to repeal the tax. Eight percent were undecided.

It was much closer among the people who saw a I-645 summary without the budget impact wording, with 44% opposed to the initiative, 40% in favor and 16% undecided.

Unfortunately for backers of I-645, the language about its potential budget impact will appear on the ballot. A last-minute legal challenge to the wording was recently rejected by the state Supreme Court in a split 4-4 decision.

Democrats in the Legislature added the ballot wording requirement in 2022, precisely to push back against tax-cutting initiatives, such as many sponsored by conservative activist Tim Eyman, which they argued did not give voters an adequate picture of impacts on public services.

Critics of the fiscal impact language, including I-645 sponsor Brian Heywood, argue it amounts to a huge and misleading thumb on the scale against any voter initiative seeking to dial back government spending.

The new income tax, or "millionaires tax" as supporters have labeled it, imposes a 9.9% tax on household incomes of more than $1 million. If upheld by voters and courts, collections will start in 2029, raising $3 billion to $4 billion a year from around 25,000 households.

One other — unsurprising — finding in the new poll: Support for the new tax goes way down when respondents are asked about the prospects of it getting expanded to lower incomes.

All 800 respondents were asked whether they'd support the tax on incomes of more than $1 million "if you knew it could eventually be expanded to apply to individuals with an annual income of $100,000 or more."

In that scenario, 41% said they'd still support the tax, while 46% were opposed.

That leaves an opening for I-645 backers in the closing weeks before the November election.

"As the measure will appear on the ballot, a majority of residents would vote to keep the income tax. At the same time, the results indicate that the contested funding statement affects how residents say they would vote, particularly among those who would otherwise be undecided," DHM research manager Kara Krnacik wrote on the firm's blog.

"Residents also distinguish between taxing the state’s highest earners and a broader income tax, which suggests the question of income taxes in Washington may continue beyond this November’s election, Krnacik added.

The DHM poll was conducted from Sept. 14-21 with results released Monday.

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