City Council Speaker Corey Johnson is not sold on a push for mandated paid vacation time to all employees in the Big Apple — fearing it could be a small business killer.

Asked whether he backs Public Advocate Jumaane Williams’ paid-vacation time plan, Johnson told WNYC’s “The Brian Lehrer Show” Monday he thinks it’s a “great goal” but “a lot of details” in the legislation still have to be “worked through.”

“If payroll costs are going to go up, and small businesses are seeing rent increases and seeing all of these costs that are not going down, how do we do it in a way that [doesn’t] adversary affects small businesses?” worried Johnson.

He was responding to “Natasha in Brooklyn,” a small business owner who called in to complain about the legislation.

“I think New York City should continue to push the envelope and be a national leader [on paid vacation time], … but a real conversation has to be had if … small businesses are closing because of rent increases — and then putting this potential cost on very small businesses that can’t absorb it in the same way a larger company with 50, 100, 500 people can absorb it,” added Johnson.

The legislation obligates employers with five or more workers to offer 10 days of annual paid leave for any reason. It would also apply to employers with one or more domestic workers as well as part and full time employees. Violators would be subject to fines ranging from $500 to $1,000.

Mayor Bill de Blasio in January first threw his support behind paid vacation time — five years after it was first introduced by Williams when he was still a Brooklyn councilman — just as Hizzoner was trying to get his quixotic 2020 presidential bid going, making it a central component of his stump speeches.