Regardless of which way the court rules, protests are likely to flare up.
All this political turmoil comes as the world's attention focuses on Brazil over its handling of the Zika virus
and the upcoming Summer Olympics in Rio de Janeiro -- and as the country struggles through its worst recession in decades.
Here's the latest on the Brazil crisis and what it means:
Who are the players?
Brazilian Democratic Movement Party: The country's largest political party announced Tuesday that it's leaving the President's coalition government, ordering its members, including six ministers in Rousseff's Cabinet, to resign from their positions.
That means Rousseff probably won't have enough votes in the National Congress to avoid impeachment proceedings stemming from allegations that she tried to hide a budget shortfall ahead of elections in 2014.
Why did the party leave? It is concentrating on "returning to its origins, finding its traditions and taking a position in favor of Brazil and the Brazilian people," said Sen. Romero Juca, the group's second in command.
President Dilma Rousseff: As well as facing potential impeachment proceedings, Rousseff provoked public outrage this month by appointing Lula da Silva, her predecessor and a close political ally, to a Cabinet post as her chief of staff.
Ex-President Luiz Inacio Lula da Silva:
The former leader, known widely as "Lula," is one of dozens of leading Brazilian political and business figures ensnared in a wide-ranging graft probe centered on state-run oil company Petrobras -- an operation known as "Car Wash."
Rousseff said a desire to harness Lula da Silva's expertise was behind her decision to bring him into her Cabinet, but critics saw it as a ploy to shield him from prosecution. In Brazil, senior political figures can only be tried in the Supreme Federal Court, meaning any prosecution against Lula da Silva would effectively be delayed if he were chief of staff.
The court will meet Wednesday to deliberate on whether to approve his assignment.
House Speaker Eduardo Cunha: He launched the effort to impeach Rousseff. But Cunha is under scrutiny by the Ethics Committee over accusations he failed to disclose the existence of offshore bank accounts to the Brazilian internal revenue service. If found guilty, he'll likely lose his post.
Vice President Michel Temer:
He's the leader of the Brazilian Democratic Movement Party, which just left Rousseff's coalition
government, but remains the only member of the party who has not been ordered to step down.
As vice president, he would likely lead a caretaker government if Rousseff were to be impeached.
But with many members of his party embroiled in the "Car Wash" scandal, Temer is not without his critics.
#RenunciaTemer (Temer Quit) became a trending topic online as social media posts pushing for the vice president to step down surged.
How did we get here?
The latest crisis began when federal police took Lula da Silva in for questioning as part of a long-running corruption investigation.
A few days later, Rousseff -- his handpicked successor and protege -- named him chief of staff, a move that largely protects him from prosecution.
That appointment prompted massive street protests. A legal battle has ensued trying to block Lula da Silva's appointment while efforts to impeach the President have gained momentum.
The ongoing crisis has divided Brazilians, bringing demonstrators onto the streets both in support of and against the government.
"I'm out here because we can't put up with the corruption anymore, and we need to step up pressure for an impeachment," business owner Thayse Kessuane, 29, told CNN during a recent protest in Sao Paulo.
"I think that things can change, and we're going to stay here until they do."
Rousseff and her supporters have described the proceedings against her government as an anti-democratic "coup."
Paulo Roberto Pepe, 55, a communications adviser, told CNN he was protesting in support of the government "because I think democracy in Brazil is being threatened."
"I'm against corruption, but the way the investigations are being carried out, we could see a real institutional crisis in Brazil."
What are the consequences?
The crisis could get a lot messier.
If impeachment proceedings move forward, they would essentially freeze Rousseff's government for 180 days while the President fights these efforts. During that time, a caretaker government would step in -- most likely headed by Temer, the vice president.
Chris Garman, head of country analysis and managing director at Eurasia Group, said his company estimated Rousseff's likelihood of being impeached at 60% to 70% -- and gave odds of 75% that she did not finish her term, including the possibility that the impeachment efforts would be defeated but new elections called.
All this uncertainty comes as Brazil grapples with its longest economic downturn since the 1930s
Brazil is also ground zero for the Zika virus
, which the World Health Organization says "is now spreading explosively
Brazil has had more than 900 confirmed cases of microcephaly -- a neurological disorder in which babies are born with small heads -- in infants born to women infected with Zika while pregnant.
And in a little more than four months, Brazil will host the Summer Olympics. It's unclear what the government will look like when the world descends on Rio de Janeiro.
On Wednesday, Rousseff's government announced that the country's sports minister was resigning from his post, another apparent sign of fallout from the growing political turmoil.
The International Olympic Committee said Wednesday it was "very confident" the games would be a success in spite of the political confusion in the lead-up.
"We are of course following political events in the country very closely and have been working in solidarity with the Organizing Committee," the statement said.
"As a result of this joint effort of the Brazilians and the Olympic Movement, we are very confident that Brazil will offer to the world excellent Olympic Games of which the whole country can be proud."
Despite the uncertainty, investors and markets seem to think a change of government could be good for Brazil, helping to turn a page on a deep recession.
They prefer the market-friendly Temer to Rousseff's left-leaning Workers' Party.