Answer:
This is actually two separate terms. The word "outcry" means a general complaint from the public, while "far cry" is an idiom meaning something of a very different nature or magnitude (i.e. distant) from another.
Example:
There was a great outcry over the increase in property taxes.
Examples:
Locking a student in the closet is a far cry from maintaining classroom discipline.
The Christmas celebration at the mall is a far cry from caroling around the town.
The weather in San Diego is a far cry from the snows of Yosemite.