LISBON — Voters twice have been presented a new school budget at referendum.

And, twice, they’ve gone to the polls and rejected it.

But not for the usual reason.

Unlike in most towns, and unlike in previous years in Lisbon, voters this year complained the proposed school budget was not too high, but too low.

In January, the Town Council directed staffs for municipal government and the local school district to present budgets lower than the previous year. On the municipal side, the directive was a $300,000 reduction. That budget was approved by the council earlier this year.

The school district was told to reduce its budget by $600,000.

The School Committee failed to deliver a budget that met the council’s directive and so, in June, after some tinkering, the council presented to voters at referendum a budget that achieved its directive of reducing the amount to be raised through local taxes by $600,000.

Voters soundly rejected that school budget.

The council sent the budget back to the School Committee, which made proposed cuts and added projected revenues but didn’t meet the $600,000 reduction mark.

The council again made changes and presented a budget of slightly more than $15 million to voters earlier this week.

Voters rejected it by a vote of 473-121. Asked in a nonbinding question whether voters felt the budget was too low or too high, they responded by a vote of 413-56 that it was too low.

In a week, the town is expected to set its tax rate for the year, a move that would lock in the amount of money the town would be able to raise from local taxes to cover spending.

According to Town Council Chairman Dillon Pesce, that means the next time the town presents voters with a school budget, likely in October, it must be at or lower than the one voters rejected on Aug. 11.

One of the sticking points in the school budget is what to do with a projected savings from an ongoing project to build a school gym that, so far, is coming in under bid.

The School Committee has repeatedly included in its budget those savings from bonds that it has earmarked to pay down debt service on the gym project which, they say, is required under state law.

The council has repeatedly removed those projected revenues from the school budget, arguing that the construction is not complete and, therefore, any projected savings is speculative surplus. The projected date for completion of the gymnasium is Sept. 25.

If voters continue to reject proposed school budgets, the school district must operate according to the most recent budget proposed by the council, Pesce said.

Traci Austin, chairwoman of the School Committee, said she feels like she is running on a “hamster wheel,” unable to make any progress on the new budget given the constraints put on the committee by the council which appears to run counter to the wishes of the local electorate.

“Now we’re kind of in a rock and a hard place,” she said. “From what I can tell, there is no avenue that the taxpayers themselves can take, unfortunately. Our hands are tied.”

She said she plans to meet Monday and discuss the apparent impasse with Lisbon School District Superintendent Richard Green, who has been on vacation.

Austin said Thursday that the school budget was slashed in 2009, when the nation’s economy collapsed. Twenty-five positions districtwide went vacant.

Since that time, “very few” have been restored, she said. The committee wasn’t able to meet the council’s goal because its budget was already cut to the bone, she said.

“As a School Committee, the majority of us felt we would not be able to without devastating what is left of our system,” she said.

The two sides disagree on many points, including the election turnout: 9 percent of registered voters. Austin called that a “good turnout” for a summer, non-statewide election.

Pesce holds a differing view, labeling the majority of the 614 voters who cast ballots in the “extremely low turnout” as a “special-interest” group, a characterization with which Austin takes issue.

As for the decision to set the tax rate on Aug. 25 rather than waiting until later in the year when voters have taken up the next school budget, Pesce said the town would have to borrow the money to operate its government in the meantime.

“We don’t have enough cash flow to keep us going,” he said. “We will run out of money if we don’t commit taxes.”