Today, Gov. Andrew Cuomo will introduce an austere state budget that is expected to be filled with deep cuts to city schools. In turn, Mayor Michael Bloomberg says education cuts will force him to lay off the youngest, most recently hired teachers first — thanks to the “last hired, first fired” state law.

Bloomberg said Sunday he may have to fire up to 15,000 teachers — every educator the city has hired over the past five years.

“And even if we didn’t have any cuts from Albany, it would call for downsizing 6,000 teachers,” Bloomberg said yesterday, adding that the city will eliminate 2,500 teachers through attrition and 3,500 in layoffs.

Meanwhile, state lawmakers are currently trying to work out a compromise that would enable Bloomberg to fire up to 4,000 “non-classroom” teachers — those facing disciplinary charges who have been removed from the classroom and those from schools closed due to poor performance. Both groups of teachers still get paid a full salary.

The compromise would be unprecedented, and allow Bloomberg to keep some new teachers. But the mayor said it still doesn’t solve the problem of skyrocketing educating costs.

“It was a nice thing, but it does not solve the problem,” the mayor said yesterday. “A small change in Albany is relatively meaningless.”

“Last hired, first fired” makes sense because younger teachers need time to perfect their teaching skills, said a spokesman for the teachers’ union.