While this expression literally means “push-push,” it has two uses that are useful to know. Let’s take a look.
1. Pushing and shoving
This means the type of confusion you’d find in big, rowdy crowds.
Houve muito empurra-empurra durante o show de rock; foi um tumulto de verdade. There was a lot of pushing and shoving during the rock show; it was real pandemonium.
Sempre quando chega um ator famoso no teatro, tem muito empurra-empurra para vê-lo. Whenever a famous actor comes to a theater, there’s a lot of pushing and shoving to see him.
This can be used in talking about politics or a contentious argument.
A comissão virou um jogo de empurra-empurra; todo mundo ficou botando a culpa um no outro. The commission became a blame game; everyone was blaming each other.
Continuou o jogo de empurra-empurra na discussão sobre o aquecimento global. The blame game continued in the argument about global warming.
Here’s an Ivete Sangalo song where she uses the expression in terms of the first meaning. There is, after all, a bit of pushing and shoving in the huge crowds at Salvador’s Carnival.