A key local need underscored with the publication of “A Portrait of Sonoma County” two years ago was access to high-quality preschool, particularly for low-income families. According to this comprehensive look at the region, only half of Sonoma County’s 3- and 4-year-old children were enrolled in preschool. Among Latino families, the number was 39 percent.

Studies routinely show that children exposed to quality child care and preschool education are more likely to read proficiently by the third grade, are more likely to graduate from high school and are more likely to go on to college and lead successful careers.

“Make universal preschool a reality” was one of the goals supervisors identified in response to the report.

Today, the Sonoma County supervisors are scheduled to take a step in that direction by discussing a proposal by the county Department of Health to expand preschool access to every 3- and 4-year-old child in the county. It’s a bold objective, but it comes with many questions. First and foremost, how would the county begin to pay for such an expansive initiative?

According to the county, the cost of preschool is nearly $13,000 a year in Sonoma County. Even if the county focuses at first, as proposed, on just providing preschool to families with a household income of 300 percent of the federal poverty level — equal to $72,900 a year for a family of four — it would cost roughly $26 million. And that doesn’t include the one-time cost, estimated at $5.8 million, to create the classroom space to provide year-round preschool for the estimated 2,013 children.

If the county moves on in future phases to expand the program to provide free education for all of the nearly 11,000 preschool-aged kids in the county, the costs could more than double.

One option is to follow the lead of cities such as San Francisco, Seattle and San Antonio, which have dedicated sources of revenue for universal preschool. San Antonio’s program, for example, is funded by a voter-approved one-eighth cent sales tax. San Francisco pays for its preschool program through a 4 percent set-aside in local property tax income, a mechanism twice approved by voters. Seattle’s program is funded through a property tax assessment.

Are Sonoma County voters ready to approve such a funding mechanism? Maybe. According to a county phone survey conducted from March 5 to March 8, roughly two-thirds of respondents said they recognized a need for expanded child care and preschool programs and would likely support a measure to fund it. County officials say the survey shows a “Sonoma County Young Children’s Services Measure” could succeed in November.

That may be true. But it also will likely depend on what other measures are on the ballot and how the county would allocate the funds. As the county notes in its report, “only quality programs have been found to produce improved child outcomes.” There is no evidence that preschool programs of average quality lead to positive results. The county would need to ensure voters that the money would be spent wisely, that classroom space would be available and that, going forward, the county’s preschool programs, like the children of Lake Wobegon, will all be above average. That may not be an easy sell.