Why do you think remote teaching takes markedly fewer people?

It should be interesting.

In a lot of states, it's not legal to leave your kids unsupervised depending on their age. I would guess that if they laid off teachers (which I think is unlikely on a massive scale due to them facilitating the online classes), then those laid off teachers might be hired as tutors or baby sitters.

I'm not so sure of this. First of all, remote learning takes just as many teachers as in-person learning unless the education plan is just "watch Khan academy and check in with us in a year." In fact under the hybrid models being proposed in areas like NYC it will take more teachers as the teacher doing in-class learning cannot simultaneously handle remote instruction. There are some decent ed-tech products out there but they can't put education on autopilot.

Second, even if you had the technology to automate remote learning during the crisis, are you going to fire all your teachers only to rehire them in Spring/Summer? No I don't have a crystal ball on the future but I'd be surprised if by Spring we didn't have some form of viable if not 100% effective vaccine. We won't be locked inside forever.

Tax revenues which have been decimated by the crisis. Unlike the Federal government which can effectively borrow/print whatever it needs, states and municipals are limited by the real world and either have balanced budget requirements or de facto requirements imposed by the bond market/fiscal realities. The equation is simple. Tax revenues have plummeted while expenses have risen due to the costs of coping with the crisis (unemployment, medical services, etc..). Am I saying all of these tax dollars are spent with great efficiency? Of course not. But imposing unnecessary austerity in the middle of a crisis has proven time and time again to do nothing but prolong and deepen economic pain. It would be arbitrary and destructive if say US defense spending can remain immune because it has access to infinite credit while our school district and firefighters will be cut because they are state/local funded.