Hugh Thomas in *The Spanish Civil War*, p. 209, gives a very simple POD for a quick Republican victory (though as he notes a quick rebel victory was equally possible):
"Nearly everywhere, the civil governors followed the example of the government in Madrid, and refused to cooperate with the working-class organizations who were clamouring for arms. In many cases, this signed the death warrants of the civil governors themselves, along with local working-class leaders. Had the rebels risen in all the provinces in Spain on 18 July, they might have been everywhere triumphant by 22 July. *But had the government distributed arms, and ordered the civil governors to do so too, thus using the working class to defend the republic at the earliest opportunity, the rising might have been crushed.* [my emphasis--DT]
https://books.google.com/books?id=4a5RAQAAQBAJ&pg=PA209