That's basically going to be dictated by the GA though, right? Rauner stamped his feet and cried for months and months over the budget/wanting to crush unions, which hurt the state even more. He's unpopular with his own party these days. I don't think he has much influence, so if the GA wanted to hike property taxes, they will.
They would almost definitely be signing Pritzker's political death warrant if they did, though. I would expect a broad income tax increase and lots more fee garbage spread around before you got a property tax hike.
I don't know how exactly Illinois got into such a hole. Other states are high tax, but they also have better services and are doing fine financially. It's not like the option is garbage state with no/crap public services or good public services and broken state. Illinois has the worst of both worlds.
But at the end of the day, at least we don't have to wake up in Indiana every day. *shudders*