It has been nearly two decades since New Yorkers faced their last doorman strike, but as the deadline for a new contract for building workers approached, the questions being posed throughout the city remained largely unchanged on Sunday. Who will safeguard my apartment as I sleep? Greet my children when they come home from school? Accept deliveries? Clean the hallways? Sort the mail? Operate the elevator? And who, for goodness sake, will let the cleaning lady in?