It is possible to overwork. We use the term workaholic when a person seems to make work their life. Some are defined by their work.
I do believe that a strong work ethic is a constructive thing, but there is a limit. Some people suffer burn-out as a result of the stress of work. The effects can be debilitating. We do need to find a balance in life that will support the balance of our thinking and actions.
Let's be prepared to die for God, but not kill ourselves in the process.
Philippians 4:5 (NLT)
5 Let everyone see that you are considerate in all you do. Remember, the Lord is coming soon.