For months, Brazilian President Dilma Rousseff and her supporters have argued that the push to impeach her is essentially a coup — an effort by Brazil's traditional elite to remove a populist left-winger from power.

They said it when she was suspended by a majority vote earlier this month, pending a trial that could remove her permanently. They said it again after center-right Vice President Michel Temer, who took over as acting president after Rousseff's suspension, assembled an all-male, all-white Cabinet in a majority-minority country.

Now a leaked recording has provided the strongest evidence yet that they were right.

Romero Jucá, Temer's newly appointed minister of planning, was caught on tape saying that he wanted to change the government in order to obstruct a massive ongoing corruption probe that implicates some Brazil's wealthiest and most powerful individuals, including himself.

"We have to stop this shit," Jucá says, per the Guardian. "We have to change the government to be able to stop this bleeding."

Jucá, who is suspected of taking $8.4 million in bribes in the corruption scandal, even brags on the tape that he has brought members of Brazil's Supreme Court and military into his scheme to oust President Rousseff.

It's unclear where this tape came from. But it's clearly authentic: Four hours after it was released on Monday, Jucá announced that he'd go on leave. It's the first major crisis for Temer's interim government — and significant vindication for Rousseff and her defenders.

What is this corruption scandal?

Between about 2004 and 2014, Brazil's state-run energy firm Petrobras — the nation's largest company and one of the largest corporations in the world — engaged in one of the most astonishing corruption schemes ever to be uncovered. That Petrobras employees and their co-conspirators thought they could get away with it speaks to just how bad corruption in Brazil had become, and how high up it went.

Nobody knows who exactly came up with the plot. But it was developed during the commodities boom of the 2000s, when oil prices were high, and involved three main groups of players: leaders at Petrobras, top executives at Brazil's major construction companies, and Brazilian politicians.

It worked in four steps:

Construction executives secretly created a cartel to coordinate bids on Petrobras contracts and systematically overcharge the company. A select group of Petrobras employees turned a blind eye, allowing the construction companies to charge Petrobras outrageous sums. The construction executives then pocketed the proceeds from these inflated contracts and rewarded their partners inside Petrobras with big bribes. Some of the proceeds also got sent to friendly politicians, as either personal gifts or donations to their campaigns. Because Petrobras is partially owned by the state, politicians can install people as executives — who then turn around and reward that politician with a bribe.

Huge sums of money, according to the New York Times, would be "hand-delivered by an elderly gentleman who flew around the world with bricks of cash, shrink-wrapped and strapped beneath thigh-high socks and a Spanx-like vest." Sometimes bribes would be distributed in the form of "Rolex watches, $3,000 bottles of wine, yachts, helicopters and prostitutes."

All in all, somewhere upward of $5.3 billion changed hands as part of the conspiracy.

How would toppling Rousseff stymie the investigations?

The investigation into the Petrobras scandal, called Operation Car Wash, has implicated politicians across the political spectrum. But Rousseff has not herself been connected to bribes, despite being chair of Petrobras for much of the time the actual bribery took place.

For that reason, or perhaps out of a sincere commitment to anti-corruption, Rousseff has given the investigation a lot of leeway. It's been run out of Brazil's Public Ministry, a unique institution established by the Brazilian constitution. Basically, it's like an attorney general's office designated specifically for cases in the broad public interest, including wrongdoing by government officials.

"Some people liken it to a fourth branch of government," Matthew Taylor, a professor at American University who studies corruption in Brazil, explained to me last month. "It has its own budget, and each of the prosecutors is autonomous — not just from the executive, but from each other."

But the Public Ministry's investigation has depended crucially on cooperation with the federal police, who are responsible to the executive branch (specifically the Justice Ministry). The former justice minister under Rousseff, Jose Eduardo Cardozo, gave the federal police a relatively free hand to participate in the Petrobras investigation — even when it threatened Rousseff's own Workers' Party (PT).

The Justice Ministry, then, has significant influence over the course of the Petrobras investigation. Which means that the president (or the acting president), who appoints the justice minister, has the power to obstruct the investigation.

And Temer, the new acting president, has an incentive to do just that, as seven out of his 11 Cabinet members have been implicated in the Petrobras scandal. Indeed, some of Temer's recent moves suggest he may already be trying to curb the influence of the Public Ministry and thus weaken the Petrobras investigation.

In light of all this, Jucá's comments take on huge significance. If you really wanted to stop Petrobras, the first thing you would do is impeach Rousseff and appoint an elite-led, possibly corrupt Cabinet. That's exactly what has happened.

Why does this matter so much now?

The Petrobras investigation fueled the impeachment proceedings against Rousseff — which is ironic, given that she isn't implicated in the scandal but many of those leading the charge to impeach her are.

But the fact that she presided over the scandal and some key members of her party helped, together with a devastating economic collapse, galvanized public opinion against her. Polling suggests upward of 60 percent of Brazilians support her impeachment.

But what Petrobras giveth, Petrobras can taketh away. If the public begins to see the push to impeach Rousseff less as a backlash against her failures, and more as an underhanded attempt to stymie the Petrobras investigation, public opinion could theoretically shift. More people could start to see Temer's government as the bigger problem, and Rousseff as the lesser of two evils.

If public opinion shifts, Rousseff might be able to survive her impeachment trial — which requires a two-thirds vote in the Senate to convict. If the vote fails, then Rousseff returns to office.

Hence why Jucá's comments are such a big deal politically: They cast the impeachment drive in the worst possible light at a time when they still might fail.