'Nanny state' is a term used by people who would like a smaller government. It indicates displeasure with the number of regulations or social programs proposed or currently in place.
The term may have been coined by Iain Macleod -- a conservative Member of Parliament -- who used it in an op-ed in The Spectator (December 3, 1965). He was complaining about a proposed reduction of the speed limit to 70 mph, but it has since been used around the English speaking world to complain about everything from Singapore controlling the press to New York city proposing smaller cups for soft drinks.