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New York Gov. Andrew Cuomo (D) is attempting to beat recently elected New York City Mayor Bill de Blasio (D) at his own game with a parallel proposal to provide free, universal, full-day pre-kindergarten. The two are facing off in a public relations and legislative lobbying campaign this week, following last week’s standoff.

De Blasio made his own proposal for a universal pre-K program and after-school programs for middle-schoolers in New York City a cornerstone of his campaign. But under his plan, the pre-K expansion would be supported by increased taxes on NYC’s wealthiest residents (those earning more than $500,000 per year), a policy that would bring in more than $500 million annually. Cuomo counter-offered with a more fiscally conservative plan (at least, relative to de Blasio’s insistence on raising taxes), instead appropriating $1.5 billion statewide over 5 years to phase in a universal pre-K program and another $720 million over 5 years from state casino revenues for after-school programs.

But de Blasio the plan, saying it’s not enough. The tax hike would be a safer way to fund the program, he argued, and he did not need to phase in the pre-K expansion as slowly as Cuomo’s plan suggests. De Blasio has pushed for full implementation within two years. Cuomo’s office countered with a blank check. “As fast as he [de Blasio] can phase in, we’ll fund it,” last week.

That got us to thinking. What might a blank check for full-day, universal, high-quality pre-K total?

The first—and biggest—relevant question: what does high-quality mean? Cuomo’s proposal identifies those programs as full-day (at least five hours per school day); instructionally aligned with the state’s early learning guidelines within 3 years; and reflective of other quality indicators, including environmental factors, teacher-child interactions, and child outcomes. Funding is based largely on the existing formula, which about $3,700 per 4-year-old child for a part-day program (2.5 hours per day), and de Blasio’s report notes full-day funding as $7,207 currently.

De Blasio’s includes many of the same quality metrics, like the use of the state’s pre-K instructional standards, evaluations of children’s learning environments, and consideration given to teacher-child interactions. But it would also be longer (6 hours and 20 minutes per school day), require additional support for English language learners and families in high-need areas, and establish a more extensive infrastructure for the Department of Education’s Office of Early Childhood Education. That’s why his per-child expenditure would be $10,239; as de Blasio notes, less than in New Jersey’s Abbott districts, Washington, D.C., or Connecticut (though still more than the average $9,342 Head Start cost per child ). Many of these are important distinctions; a report published last year, , found that the quality of pre-K programs is essential to recouping its costs.

New York has about . We split that figure in half to estimate about 237,000 4-year-olds reside in the state. Even in most universal pre-K programs, like , enrollment tops off around 75 percent (though UPK program is closer to 80 percent). So for these purposes, we calculate that the state would need about 178,000 seats to achieve universal pre-K – about 75,000 new ones when you subtract out the . Since those existing seats are only funded for half a day by the state, we doubled the per-child expenditure currently used (using the $7,207 figure) to find the costs of the expansion, and added it to the costs of the new seats.

In total, our back-of-the-envelope estimates show the cost would be around $900 million per year, once the state is operating at full capacity. (Admittedly, the phase-in years would likely be far lower, so Cuomo’s $100 million for year one and $200 million for year two may not be as unreasonable as they first seem—unless de Blasio pushes children into classrooms faster than he can likely recruit and train their teachers.)

But there’s another key consideration, as well: political and logistical feasibility.

It seems both the Cuomo and the de Blasio plans still probably undersell the full cost of a universal pre-K program. And there will be other costs, like construction of new classrooms and recruitment of new teachers. Gov. Cuomo announced a $2 billion bond act to bring technology to schools, some of which could be used to build new pre-K classrooms – but of course, that relies on the voters. Meanwhile, de Blasio’s proposal would take the funds out of the new tax revenue by appropriating about $97 million in the first year to the new costs of building classrooms and recruiting new teachers, raising questions about the sustainability of those efforts to recruit and train teachers.

But Cuomo may not be underselling it by as much as de Blasio thinks in the initial first years, given how difficult New York will probably find it to gather enough qualified teachers to expand the program as quickly as he proposed. The mayor’s zeal for rapid pre-K expansion may indicate the inexperience of a new executive – the mayor has rarely, to date, had to deal with the practical concerns of implementing policies.

Still, underestimating those costs could turn out to be expensive for Gov. Cuomo; now that he’s offered de Blasio a “blank check” for implementation, the mayor could use it to push well beyond the state’s opening pre-K funding offer. And since pre-K is typically a popular push among voters and residents, Cuomo’s attempt to remove some of the political barriers by funding it outside a tax hike could speed up the process.

So even if both have underestimated the annual costs of a universal pre-K program, de Blasio has asked for a much larger, more politically charged request, one that may be beaten back at the first sign of life by those who oppose a significant tax increase on high-income households. Between political infeasibility and its huge costs, universal pre-K programs in either New York City or state may have a much longer road to travel.