St. Paul voters will be asked this fall to dig deeper to help cover school-district costs — deeper, in fact, than a recent survey indicated many were willing to pay.

The school board agreed Tuesday to put a proposal on the November ballot to boost its annual operating levy by $475 per student. That would raise an additional $18.6 million annually for a school system battered by deficits, and staff and program cuts, for four years running.

But the potential tax impact on the city’s average-valued $175,000 home would be $136 per year, according to district estimates. That number is significant because the request falls between what a majority of survey respondents said they were and were not willing to support.

According to the survey conducted this spring by consultant Springsted Inc., 58 percent of respondents said they would back a $125 per year tax hike. But when asked about a potential $150 per year increase, the support dropped to 44 percent.

Still, the odds of board members pushing for more than what a $125 per year tax increase could generate were heightened in June when they put the final touches on a 2018-19 budget that showed a $17.2 million deficit at the start.

A $125 per year hike would generate nearly $17 million annually, just about the size of this year’s shortfall.

Board Member Mary Vanderwert said then that she did not run for office with the intention of shrinking the state’s second-largest school district. Steve Marchese, elected along with her in the Caucus for Change movement of 2015, said he, too, believed that a proposal to raise more revenue from voters should be sizable enough to strengthen the district and move it forward.

The constant cycle of budget slashing “cuts into our soul as a school district,” Vanderwert said Tuesday. She said that while it was “unrealistic” to ask for more in a referendum, she wished the district could do so to deliver “all those things we dream for our kids.”

If voters back the proposal, the district pledges to not only limit future budget cuts, but to also improve its middle schools and increase mental health and social-emotional supports for students, among other pursuits, Superintendent Joe Gothard said.

If the measure fails, multimillion dollar budget cuts would continue, he added, and the district would be hamstrung in its ability to implement a new strategic plan that includes a call for a renewed focus on the middle schools.

Sixth grade has been when many parents pull their kids from the district and send them to other school systems or charter schools.

The St. Paul Federation of Teachers is prepared to help in get-out-the vote efforts. It has also worked with the district this summer to deploy people to go door to door to talk with families in an effort to boost enrollment numbers.

The Minneapolis Public Schools also plans to go to the voters for more money in the fall. In June, the school board approved two referendum questions for the November ballot — to increase the district’s operating levy by $18 million a year and to create a $12 million technology levy.

Districts have been forced to rely on voter-approved operating levies to make up for what they argue is a lack of state support.

According to Gothard, if the state’s general education funding had kept pace with inflation, St. Paul Public Schools would be receiving nearly $550 more per student in 2018-19, or a total of $19 million.

Board Member Marny Xiong said that people have shown they’ve had “the back of our educators.” She noted students were the city’s next leaders. “We must do this for our kids,” she said.

The Springsted survey showed stronger support among people whom the firm described as “very active voters” — those who’ve taken part in at least six of the last nine elections — saying that 50.4 percent were willing to back a $150 per year increase.

St. Paul’s current levy is $705 per student, or about $320 per student less than the metro district average.

Voters last approved a levy increase in 2012, and the price tag then was about $66 per year on the average-valued home. That proposal had the backing of the mayor’s office and the St. Paul Area Chamber of Commerce, and was to last the district eight years.

The operating levy to be voted on in the fall would replace that levy and run for 10 years. It also would include annual inflationary increases.