It´s not work like that. The militaries couldnt be more quiet.
Lula (and his party PT) had a big time support to become president in 2002 elections. At the begin, he was a lot popular until the corruptions scandals start to appear to public.
First, there was a scandal called Mensalão, where a lot of PT personalities were arrested due corruption. Despite, Lula was so popular that he could reelect himself and make his successor (Dilma, the present president).
The fact is that the scandals increased since an police operation called Lava Jato discovered that PT was changing big contracts with Petrobras (biggest brazilian state company) for money beside tons of another ilegal operations.
A lot of big time business men were arrested and they already confessed their crimes. These crimes were also investigated and proved in international basis (most of the robbed money were moved to Switzerland that is returning the money to Brazil). Finally, the investigation was able to find the politics side of the corruption (Lula was benefited with proprierties and Dilma´s presidential campaigns were supplied by this money).
So, PT that was so popular, nowadays are hated by 75% of the brazilian population. There are also an impeachment process and several criminal process against Lula and PT politics. In one of these process, a judge decided to bug Lula´s phone and discovered a lot of ilegal and unconstitucional pratices (like the fact that Lula was appointed minister by miss president only to delay the criminal process and prevent his arrest).
Because that PT started to scream that the brazilian upper classes are trying to take the power ilegally. They tell that everybody robs and that they didnt invented the corruption in Brazil. So, basicly people are trying to take them from the power because Lula was poor sometime in his life and people are envious.
All in all, PT are trying to paint the process as political and the judge as a kind of devil. They have only the support from some big works unions (they are very confused with PT and dont really represent workers interests) and from some lefty "intelectuals" who are so arrogant to admit that their recent support to PT was a mistake.