ALBANY – Housing is displacing bail as the big issue holding up a state budget 13 days past an April 1 deadline, a source familiar with the discussions told The Post.

Gov. Kathy Hochul is pushing an affordable housing plan aimed at creating 800,000 new units over the next decade despite resistance from suburban lawmakers annoyed at an approach that would undermine local zoning laws.

The governor signaled Thursday she’s not about to back down.

“As I’ve said from the beginning, the right budget is more important than an on-time budget,” Hochul said at a press conference outside Albany.

“I’ve laid out my priorities about how to make New York safer, more livable, and more affordable. And that’s the budget I plan to deliver,” she added at the event announcing new federal funding for a Capital Region bridge.

The state Capitol. meanwhile, has been virtually empty of rank-and-file legislators since Monday, when Albany Democrats approved a budget extender keeping state government going as negotiations continue on a spending plan expected to hit a record-smashing $230 billion.

A focus on housing rather than bail would be a notable change from discussions over the past week, when controversial limits on cash bail dominated three-way talks between Hochul, Assembly Speaker Carl Heastie (D-Bronx), and state Senate Majority Leader Andrea Stewart-Cousins (D-Yonkers).

The two issues have largely held up talks behind closed doors on other touchy topics — like expanding charter schools, funding the MTA, and raising taxes on the wealthy, legislative leaders said earlier this week.

Hochul is pushing to eliminate existing law that says criminal defendants must get “least restrictive” conditions to ensure they return to court despite legislative resistance to amending 2019 bail laws reform, which critics blame for contributing to rising crime.

“We’re very close to a general agreement,” Stewart-Cousins said Tuesday about the status of bail talks.

Housing is another matter.

Hochul has proposed downstate and upstate localities hike their housing stock by 3% and 1%, respectively, over three years. Failing to meet these goals would mean a state board could override local vetoes on construction.

A second proposal would allow higher densities – roughly 50 units per acre – within a half-mile of commuter rail stations within 15 miles of New York City.

Experts say an enforcement mechanism is critical to making a housing plan succeed.

Suburban lawmakers have pushed back against the proposal though legislative leaders appear willing to strike a compromise deal with Hochul.

Stewart-Cousins has said her Democratic supermajority could support a proposal with fewer sticks and more carrots — like the $500 million in grants, legislators have floated to encourage localities to build by giving them help to expand infrastructure like sewer systems.

“There is more incentivization that is needed for communities to really understand what it is that is needed and how we can achieve the goal collectively. That should be done before we actually started doing sticks,” she told reporters Tuesday.

Heastie noted the day before that legislators have plans of their own for the governor to consider, with progressives pushing for a final budget to include controversial “Good Cause” eviction legislation to limit rent hikes statewide despite protests of landlords.

“There’s a lot of things on housing, including tenant protections,” he said.

“The [rental assistance] issues concerning NYCHA, other types of housing that we would like to see being developed – a new Mitchell-Lama program – so it’s an extensive list,” he added while referencing an affordable housing program focused on middle-class people.

Hochul said Thursday she’s in Albany ready to deal with lawmakers in the coming days to break the budget stalemate.

“We’ve been working around the clock my team has not left town. We’ve had many many meetings ourselves internally – just came from one. Our teams are doing a lot of Zoom calls with others who are not here, and we’re going to work hard through the weekend,” she said.

A Heastie rep did not respond to a request for comment about when he would be back in the Capitol. Stewart-Cousins is expected to return Friday.

Staff from both their offices have remained in the Capitol this week.

“The leader and her team have been engaged with the governor since before the budget and during this entire process and we have always been willing to meet with the governor and her team,” spokesman Michael Murphy said.

Republicans, meanwhile, are throwing shade from across the aisle at Democrats who weren’t in the Capitol crafting a budget deal Thursday.

“Typical of the secretive, closed-door process that Albany is known for,” said Assemblyman Ed Ra (R-Garden City), the ranking GOP member of the Ways and Means Committee charged with fiscal matters.

“Disgraceful and an insult to New York’s taxpayers,” state Sen. Thomas O’Mara (R-Elmire), the ranking GOP member of the Finance Committee, added about the hold-up Thursday of a final budget deal.