Anyone even conceptualizing the thought, "Illinois is being run by a Republican governor," should be disqualified from this discussion. This state has been run exclusively by Democrats for many decades. The voters chose a Republican governor this time around in a grudging acknowledgement of total Dem failure. His every proposal has been met with resistance, ridicule, etc. This pile of shit is totally the property of the Democrat Party of Illinois.
Having said that, the only solution is some form of quasi-bankruptcy - probably enabled by Federal Legislation - wherein the state is taken over by an appointed conservator, who would have absolute power to tear up any and all contracts, including public employee contracts and their associated pension provisions. No legislation could be passed without the approval of the Conservator, and a balanced budget would be an absolute requirement.
This crisis calls for a creative, drastic, painful solution. Then do the same thing in Puerto Rico.