After some digging, I realized that just 10% of the population pays about 71-72% of the taxes.
If half of that 10% of the population leaves, the city will have 1/3rd less tax revenue (it will have less than 65% of the current revenue). Also, the city will be limited on what it can tax, as if it raises the taxes more, even more people will leave for low tax states and turn it into a death spiral. The only way to get out of the situation is to have help federally.
Meanwhile it will have to cut services drastically.... from trash collection, social services, schools, etc... Apart from the slow trash decay, I think the first shock from some of the folks will be when MTA is forced to raise fares to $4 or $5 (now it is $2.75).
As for those 'let the gentrifiers leave' populist folks, Sure, rents will go down by 15-20% but a lot of the folks will be jobless soon, and manny other things will get more expensive.