OLYMPIA — The most sweeping plan yet from anti-tax activist Tim Eyman was soundly rejected Tuesday as voters appeared unwilling to put government on a forced diet of limited revenue.

Initiative 1033 — the latest in a long line of measures sponsored by Eyman since the 1990s — proposed a growth cap on revenue flowing into the main checking accounts of city, county and state government.

Eyman acknowledged defeat Tuesday night as unofficial returns showed I-1033 being defeated by about 55 percent to 45 percent, with 48 percent of the expected vote counted.

The opposition campaign declared victory, saying voters already had seen government make significant service cuts in the face of a brutal recession.

“I think people looked at the recession’s impact in their communities — be it fewer teachers in schools, or more potholes in their road — and they asked themselves if Initiative 1033 would make those impacts better or worse,” No on 1033 spokesman Scott Whiteaker said.

The opposition campaign featured a broad coalition of establishment figures — including elected officials, labor unions and big business — arguing that Eyman’s measure would lock governments in a “permanent recession.”

The campaign spent more than $3 million to air its message around the state, including a big donation from Microsoft Corp. co-founder Bill Gates.

Eyman argued that the initiative would ensure government didn’t go on a spending spree once the economic recovery sent money flowing back into the treasury. He still claimed a moral victory Tuesday, pointing out that I-1033 was getting thousands of votes despite zero campaign spending from his side.

While acknowledging that “we’re not going to have 1033 as a tool in our toolbox,” Eyman said politicians should not forget that about 45 percent of voters were still supporting its strict caps on government revenue growth.

“If Olympia views this as ‘Goody, voters are actually in favor of higher taxes,’ they are seriously misleading the electorate,” Eyman said.

Had the initiative passed, the growth in revenue collections at the state, county and city levels would have been pegged to price inflation and population increases.

Any taxes collected above the cap would have automatically flowed into a separate account, which would replace property tax revenue in the following year, giving property owners a break on their bill.

Governments could collect revenue above the limit only by getting voter approval for new taxes. Some sources of income would be exempt from the cap, including the state’s constitutionally protected Rainy Day Fund and federal money to the state.

An estimate from the state Office of Financial Management said I-1033 could have diverted nearly $6 billion away from the state general fund over six years. Cities would have lost about $2 billion during that stretch, and counties would have lost close to $700 million.

For some voters in strongly Democratic Seattle, Eyman’s name alone was almost enough to draw a “no” vote.

“I tend not to side with Eyman,” said Krista Means, a 41-year-old stay-at-home mom. “When I was reading the voter’s pamphlet, I thought they should take his name out of there, that alone will make people not vote for him.”

But Bob Couture, 61, said he voted for I-1033 because government has been spending too much money on its way to nearly across-the-board deficits.

“We need spending restraints, maybe (I-1033) goes too far, but look where we are now,” he said.