In elections PSD/PTB ran together against UDN and continually won. PSD had taken power in 1945 and 1955, and PTB in 1950. Because of this UDN sided with any officers with rebellious intents. In 1960 UDN allied with the minor PTN and managed to elect Jânio Quadros, a populist wildcard, who did not rule in the UDN's style. In any case he was quickly out and PTB got in power, but castrated by the parliamentary system. In 1963 a plebiscite restored presidentialism and Goulart embarked on a radical agenda of fiscal, electoral, urban and land reform.
At the same time the existing economic model had run into its contradictions. In part because of the heavy spending of the 50s there was uncontrolled inflation and budget and foreign exchange deficits. Foreign investment diminished and per capita wealth had just begun to contract. Strikes doubled from 1962 to 1963. There was land conflict in the hinterland. The middle class was also restless and opposed the government. There was an atmosphere of radicalism.
Goulart's reforms enraged elites and were blocked by the conservative Congress. The majority of media and the Church as well as the American embassy would later back the coup. Goulart was limited to his political base, with most stakeholders in society against him. In 1965 there'd be elections and PTB would join as a junior partner to PSD, with opinion polls indicating they'd win, but Goulart now wanted to steamroll the political system to get his reforms ahead, possibly implementing re-election or even a Constituent Assembly.
This required rousing up radicals to put pressure on Congress, essentially doing his own coup, and so in the early months of 1964 he was on a busy sequence of rallies with unionists, activists and the like. Rallying supporters in the military was an important part of that, which motivated his leniency with the sailors' revolt and his speech at the Automobile Club. He also counted on having stacked the upper echelons of the military with apparently loyal men. Communists were not directly part of his circle but also backed him.

Communists in the military formed the "Setor Mil". The party could count on about 100 active officers, 20-30 in higher ranks. They had feet in the National Security Council and the Military Cabinet. In the Air Force they had 20 officers, including 2 brigadiers and 3 colonels. Most important was brigadier Francisco Teixeira, who commanded the powerful IIIrd Air Zone in Rio de Janeiro.
Jango's most important support base among sergeants was of leftist nationalists. High-ranking legalists also included moderate PSD types.
The rebels, in turn, were on the right, but not necessarily liberals like the UDN. Their governments would later embrace strong spending with massive public works (even repeating 60s inflation in the 80s, now even greater) and a strong state with a number of public companies and directed national policy towards rural and industrial settlement on the hinterland, reducing dependence on hydrocarbons through nuclear power and biofuels and so on. They'd find themselves divided among moderates, who wanted to set things in order and return power to civilians, and hardliners who had a broad interpretation of setting things in order and thought it would take many years. The first ones to rule were the moderates.