Noun for people/employees/coworkers who tend to say "it's not my job" when asked to do something slightly beyond their norm?

You could also consider jobsworth.

Wikipedia's entry is illuminating:

"Jobsworth" is a British colloquial word derived from the phrase "I can't do that, it's more than my job's worth", meaning taking the initiative and performing an action that is beyond what the person feels is in their job description.

In my experience, it has two overlapping meanings:

1. Refusing to do anything other than what is absolutely required of them by their job description
2. Deliberately using technicalities of a rule or job to obstruct reasonable activity

It may be British English only: I'd be interested to hear whether this is in use in other English-speaking nations.

Shirker comes close. From Dictionary.com:

a person who evades work, duty, responsibility, etc.

The term doesn't necessarily specify a particular method of avoidance, though, so your not-my-jobber would be a sub-class of shirker.

Edited to add this great little poem from a 1921 Railway Signal Engineer issue (attributed to Selected):

THE SHIRKER

“That's not my job, and it's not my care,”
When an extra task he chanced to see;
“That's not my job and it's not my care,
So I'll pass it by and leave it there.”
And the boss who gave him his weekly pay
Lost more than his wages on him that day.

“I'm not supposed to do that,” he said;
“That duty belongs to Jim or Fred.”
So a little task that was in his way
That he could have handled without delay
Was left unfinished; the way was paved
For a heavy loss that he could have saved.

[etc.]

which sounds very much like the kind of individual you've described.

To tell you the truth, I call such people problem employees.

I like @1006a's answer, but I'll offer up slacker as an alternative word, if not meaning.

From Dictionary.com:

slacker: A person who evades his or her duty or work; shirker

A slacker is a person who will use any means necessary to avoid work. A slacker would certainly use it's not my job "as a crutch to prevent extraneous exertion of effort".