Unions, represent the currently employed, push wages above the market price and therefore increase unemployment to the detriment of those not employed.
Of course Union leaders are worried about cuts in public spending because this directly affects the power and pockets of the unions. Unions represent a small proportion of the working public. The government represents the majority of the public and is in effect the union of the majority.
One of the problems with unions striking is that they are a selfish thing to belong to. Usually Employees, company's and the government are represented, but not the public.