Yes, Flavia, it would sound strange.
When the going gets tough = When life is harsh, when you are facing lots of non-specific difficulties, when you are out of work and in poor health, when you can't find a job and you owe money, etc. It is all very non-specific. Ah.... I just thought of something: "When life gives you lemons...." By "lemons" we mean bad luck, bad health, broken romances, a death in the family, the loss of employment, etc. Very non-specific. It could refer to anything.
The tough get going - Strong people react and work hard, achieving new goals.