Internal or External conflict? An employee having to work against a very tight deadline

I believe it would be external

This is an external conflict. An external conflict happens between a character, in this case the employee, and some external obstacle or challenge. This challenge can be a person, animal, thing, or something a bit more abstract like a deadline.

An internal conflict, on the other hand, is between the character and his or herself, perhaps due to opposing values or goals. In this case, the employee might be conflicted between working on the deadline or just quitting her job and moving to Bora Bora (she should choose the second one)