The New York City Council is set to override a mayoral veto on Thursday afternoon that will nix the waiting period of the Big Apple’s housing voucher program and expand its eligibility criteria.

The vote comes three weeks after Mayor Eric Adams broke out his veto stamp in June in an attempt to block of the legislation, complaining that lawmakers had overstepped their authority and that the package could cost the cash-strapped city billions of dollars.

Lawmakers are expected to formally take up the matter during their regularly scheduled afternoon meeting.

“We will override this veto and I hope Mayor Adams is listening right now — you cannot lead the greatest city on earth and deny people the right to housing,” said Councilwoman Carlina Rivera (D-Manhattan) at a rally outside of City Hall just hours before the votes are expected to be cast.

The four provisions passed by the Council and that Hizzoner subsequently attempted to nix would end a provision that requires people to stay in a shelter for 90 days before becoming eligible for a voucher.

Amid the fight, City Hall eventually embraced that policy change and implemented it as a tweak to municipal regulations through the mayor’s executive powers.

The rest of the package the Adams administration bitterly opposes.

“[W]e had several conversations with the council and really tried to show them why the existing legislation that they pushed forward was problematic,” the mayor told reporters Tuesday at an unrelated press conference in Brooklyn.

However, Council sources say Adams and his aides made little effort to try and find the votes to sustain the veto until this week.

Beyond nixing the shelter-stay requirements, the measures would allow New Yorkers eviction to apply for a housing voucher without first entering the shelter system, bar landlords from deducting the cost of utility bills from a voucher check and slightly increase the income-level cutoffs to qualify for the assistance.

City Hall estimates the four bills combined carry a price tag that could reach $17 billion over five years, a tally fiercely disputed by the sponsors of the package. The Council’s own budget projections peg the cost at $10 billion over five years.

Lawmakers originally passed the package with a veto-proof majority in May amid a furious back-and-forth between the Council and City Hall — setting the table for Thursday’s showdown.

“It would really be unfortunate if the Mayor chose to veto the bills that help New Yorkers leave the shelter system,” said Council Speaker Adrienne Adams (D-Queens) at the time, just before the first votes were cast then.

“We’ll cross that bridge if and when we get there.”