As I recall, only 1-2 years ago, the Manager of a large centre somewhere in Australia, suggested it was indeed the controllers problem - that their was an expectation not to refuse reasonable overtime. Reasonable overtime was then determined to be one 8 hours shift every fortnight - that is 20+ extra shifts a year.
A further suggestion was implied that refusal could be constituted as illegal industrial action - not sure that this was tested, however I have seen extreme pressure being applied over the phone by some of the prairie dogs to some of the more recent arrivals to get them to come in. The older guys generally "have just taken the top off a coldy sorry (hic)". (At 7am!)