Talk of a truce in Minnesota’s preschool policy war — now in its fourth year — evidently was premature. Republican majority legislators and DFL Gov. Mark Dayton fired new salvos Monday, revealing that they remain deeply at odds over how best to spend state tax dollars to advance the learning of this state’s youngest citizens.

Leaders of the House Republican majority engaged two big guns — Ecolab CEO Doug Baker and former Minneapolis Federal Reserve senior vice president Art Rolnick — to help tout a $24.6 million increase in funding for scholarships to low-income families, to be spent on quality-rated programs serving children between birth and age 5.

The House GOP budget also includes an $8.5 million increase in School Readiness — funds that flow to school districts to help pay for a variety of programs for 4-year-olds. But it rejects Dayton’s preferred approach for 4-year-olds — an additional $175 million to allow all willing districts to provide tuition-free pre-kindergarten. Under the House budget, the 75 school districts whose pre-K programs were funded by the 2016 Legislature at Dayton’s insistence would receive less specific School Readiness funds instead.

Dayton countered by circulating 20 recent statements by Greater Minnesota educators and parents supporting public school pre-K and underscoring the statewide reach of his approach. He reiterated that pre-K is his priority for new spending — while House Speaker Kurt Daudt said, “If we are going to spend more money, [scholarships] are our priority.”

We hope Daudt was signaling a path toward compromise on work that arguably holds the greatest promise to narrow Minnesota’s persistent educational achievement gap. Dayton is right to call for more early ed spending. The Star Tribune has recommended directing at least $50 million more in the next two years to the state’s little learners.

But Daudt and the GOP have the better idea about how to spend the bulk of those funds. Sound research has concluded that scholarships for low-income children from birth to age 5 produce a higher return on investment than does universal preschool. This state’s neediest children should have first claim on public resources.

That said, a good case can be made for public preschool programs in places where high-quality private preschools are in short supply. Lawmakers would do well to apply a means test to public school programs as well as to scholarships, so that in both instances dollars flow to people and locations that need them the most.

Public resources are perennially scarce; priorities always must be set. But GOP lawmakers allow an assumption of scarcity to drive their early education argument even as — in the House — they’ve advanced a tax bill that would take $1.35 billion out of the state’s general fund through mid-2019.

That assumption deserves to be questioned. A number of GOP-dominated states — among them Florida, Georgia, Oklahoma and West Virginia — now offer universal preschool for 4-year-olds. On Monday — as Dayton and Daudt quarreled — New York City’s mayor announced that free preschool would be available to all of his city’s 3-year-olds within four years. It would build on that city’s free pre-K for 4-year-olds, which Mayor Bill de Blasio considers a top accomplishment of his first term.

Minnesota needs to keep pace on early ed now, or it could find itself playing catch up for many years to come.