[jeffrallen]

I learned the term while learning french, working for Médecins sans Frontières Suisse. It was most definitely translated as démerde, not débrouiller.

[crubier]

I'm french, and both "se débrouiller" and "se démerder" mean exactly the same thing. "se démerder" is just more familiar/foul.

[eric-burel]

I would mostly use the familiar version if someone or an organization explicitly created the situation, like I must go to the post office but it's only open during my work hour, and closed the only day I can take an hour off. And System D is really débrouille to me