Well, my gut response to Putsch was that was not a word, since it is capitalized, but then I remembered it was of German origin, where they capitalize all their nouns. My second response was what was wrong with coup? And therein lies the rub.
Coup comes from the Greek "kolaphos" for a blow or slap, through the Latin "colaphus" for a cuff or blow to the face/ear, and ultimately through the old French "colp" for "to cut or strike". It's not hard to imagine how a physical swift, unexpected slap to the face which impugns ones dignity could be used to mean a metaphorical swift, unexpected slap to ones dignity by removing someone from power. Meanwhile, Putsch comes from the same word in Schweizerdeutsch meaning a violent blow or push, from onomatopoeia for the action. Both definitely have the implicit meaning of usurping power in some manner, but Putsch is more violent in its origin than coup, a push being more physical than a slap, and therefore, a Putsch may be effect by mere brute force of numbers, while a coup is usually associated with a smaller group. Also, Putsch need not be sudden, unlike coup, which is unexpected to the recipient. Finally, Putsch evolved specifically in 1830 relative to a revolt in Zurich, while coup has existed to describe any clever, successfully executed but unexpected plan since c. 1400. Therefore, Putsch only refers to government overthrows, while coup has broader usage, even though it is colloquially immediately associated solely with government overthrow.
So, while I may not have much need for the use of Putsch, largely because so few people will know what the word means, and might think, since I can pronoun it with a proper German accent (I'll work on my Schweizerdeutsch later), that I am merely saying "push", coup has so much more potential. Was it a Putsch to try to impeach Clinton? This past senatorial election was a Putsch to the Republican leadership. Yes, and yes. But these sentences would sound just as good, and a bit more understandable with "coup". Was it a coup to try to impeach Clinton? The Democratic party mounted a coup of the Republican leadership in the last senatorial election. It may not have been sudden, but it was definitely unexpected to many. His attempted coup to have the house for an evening of beer and poker by encouraging his wife to go to the movies with her friends failed when she discovered the keg in the garage. Perhaps, but plan or scheme works better. It was a real coup to get the celebrity endorsement away from his competitor. This is a common expression, even without the express idea of taking it away from someone else, which is otherwise implied. Knowing that it was going to be cold that night, she staged a coup to get all the covers. Yes.
And again, while I don't do phrases or foreign languages, and particularly not the combination of both, I will make a passing reference that "coup d'etat" and "coup de grace", both French, utilize the meaning of "blow" for "coup", but still retain the meaning of taking power, either from the state (d'etat) or a final act (de grace).