I think you're missing a lot here. The city isn't failing for lack of jobs, but for lack of jobs that produce value. A job rebuilding the infrastructure of an area is only valuable if there are other jobs from which you can tax to justify that.
If I spend $100 million to fund a trench that does nothing, it's a money sink. I've effectively thrown that money away. However, I have achieved however much employment that $100mm bought me. Until and unless that $100mm gets somebody some value, it isn't worthwhile, and as we've seen, there are very few people willing to fund completely pointless projects for no reason... even governments try to avoid it.
This is different than health care spending, or housing, or welfare -- those things (at least arguably) provide benefits. If I give someone health care for free, it's largely assumed that the cost of that health care will be offset in other ways. See the discussions on the Utah Unemployment article for examples.
But because governments are funded by tax dollars, and tax dollars are generated by earnings, until and unless people are earning moneys from outside the government that pays them, it simply isn't sustainable. Building infrastructure in the middle of nowhere is fruitless it is used as a lure for some form of money or productivity. The absence of said productivity means that, at best, you'll be revenue neutral on the funding projects and sustainable until inevitably inflation wipes everything away. Of course, to do that, the community has to be entirely self sustainable, which Flint definitely isn't.
In short, tax and spend can't work unless there's something to tax that isn't also part of the spend.