Mayor de Blasio climbed to power by promising to expand prekindergarten through a tax on the wealthy and to clamp down on charter schools. But voters aren’t in agreement with him on those issues now, according to a new poll.

In the wake of the city’s recent and fiercely debated decisions to keep schools open during snowstorms and to deny public space to a few charter schools, a majority of those voters now disapprove of the way de Blasio and his education chief are running the school system, according to the survey by Quinnipiac University.

The poll found that 55 percent of voters with children in public schools disapprove of the way de Blasio is handling the school system, compared to about half of all surveyed voters. The mayor’s overall job approval rating is 45 percent, according to the same poll.

Forty-five percent of those public school parent voters disapprove of the way Chancellor Carmen Fariña is doing her job, compared to 36 percent of all respondents.

The survey showed very strong overall support for de Blasio’s plan to increase access to pre-kindergarten. But it also underscored voters’ preference for Governor Andrew Cuomo’s plan to fund that program without raising taxes rather than for de Blasio’s plan to tax the wealthiest New Yorkers, with 54 percent backing Cuomo’s plan and 35 percent backing the mayor’s.

That’s a shift from the Quinnipiac poll released in mid-January, which found that 74 percent of voters approved of the pre-K tax. Public support for the tax appears to have eroded as its odds of passing through the state legislature grow slimmer and as Cuomo promises to fund a pre-K expansion at the scale de Blasio seeks but without the tax.

The new poll also shows that voters are still split over whether the city should have more charter schools, but they don’t necessarily want the schools to pay rent. Among voters with students in public schools, 54 percent say charter schools shouldn’t pay rent to operate in public space. Among all voters, 47 percent think charter schools shouldn’t pay rent, up from 43 percent last October.

That follows the city’s decision to block plans for a few planned Success Academy charter schools, spurring an outpouring of support from charter school backers and the governor.