Nah they could. I’ve lived in four different states and IL by far has more public employees per citizen than TX or AZ. Only NY is less efficient.
How much of that is efficiency (fewer workers needed to provide a given unit or level of service) and how much of it is providing fewer public services? I've lived in Mass, IN, and IL, and I got the impression that there were a lot of public services in Illinois that we didn't necessarily have in the other places (from pottery classes at the parks district to a larger number of state-supported passenger trains and, admittedly based on just a few visits, shorter wait times at the DMV in Illinois than anywhere I ever lived).
The right amount of public services is a value judgment. The right number of employees to provide a given level of service (and their pay and benefits) is a human resources-management-labor relations decision. The right number of employees per citizen is therefore a mix of both.
My experience of state and local budget cuts in Mass and Indiana is of losing services I liked: my art teacher and gym teacher in 2nd grade, Sunday service on my nearest bus line and commuter rail line in high school, library hours, parking lots and bathrooms at nearby parks, hours at the city nature center, city leaf pickup, having to pay a special fee for trash hauling. Now maybe those cities and states could have found ways to save money without cutting services; most organizations tend to build up too many administrators who don't add much value, for example, I can totally believe in a situation where the managers of a state department would protect their jobs rather than the jobs of the people providing the actual services when the crunch came, because "we must have a deputy director of x". Or maybe they could have helped the line workers to do more by, for example, reducing paperwork requirements. Or maybe there was some featherbedding to get rid of. But I find it really hard to believe that there are enough useless workers to allow for cutting 10% of Illinois' state budget without cutting anything except useless workers, especially when we remember that a big chunk of the budget goes for things other than state workers: supplies, utilities, maintenance, rents, etc., etc. For me budget cuts mean service cuts.