Story highlights

NEW: Brazil's high court says a judge doesn't have jurisdiction to investigate Lula da Silva

Government supporters gather in capital as impeachment commission meets

Protests are planned in five states Thursday in support of embattled President

Rio de Janeiro CNN  — 

The political future of Brazilian President Dilma Rousseff hangs in the balance as lawmakers consider a request to impeach her and she waits to hear whether the country’s Supreme Federal Court will deal her a significant setback.

The court is considering whether to allow Rousseff’s appointment of ex-President Luiz Inacio Lula da Silva to her Cabinet, a move that would help shield him from prosecution while he is under investigation in a wide-ranging graft probe.

Rousseff is also facing maneuvers in the National Congress to impeach her over allegations that she tried to hide a budget shortfall ahead of elections in 2014.

Hundreds of government supporters carrying red banners bearing the logo of her ruling Workers’ Party gathered on the lawn Thursday before the Congress in the capital, Brasilia, where the impeachment commission was hearing the testimony of government witnesses.

Supporters plan to stage demonstrations in five states across the country Thursday in solidarity with the embattled President.

The ongoing crisis has divided Brazilians, bringing huge numbers of protesters onto the streets, both in support of and against the government.

Brazil in crisis: Five reasons Dilma Rousseff should be worried

Sports minister quits

Rousseff’s government was dealt a smaller blow Wednesday when Brazil’s sports minister, George Hilton, resigned a little more than four months before the start of the Summer Olympics in Rio de Janeiro.

Why is South America’s largest country in such a big mess?

Ricardo Leyser, a senior official in the Sports Ministry, will replace Hilton on an interim basis.

The International Olympic Committee said it is following political developments inside the country but expressed optimism that the games will go on as planned.

“The Brazilian people will deliver a memorable Olympic Games full of their passion for sport for which they are world-renowned,” an IOC statement said. “We are very confident that Brazil will offer to the world excellent Olympic Games of which the whole country can be proud.”

A ‘coup’

The latest episode in Brazil’s political upheaval began when federal police took Lula da Silva, known widely as “Lula,” in for questioning this month as part of a long-running corruption investigation.

Lula da Silva is one of dozens of leading Brazilian political and business figures caught up in the probe centered on state-run oil company Petrobras – an operation known as “Car Wash.”

A few days later, Rousseff – his handpicked successor and protege – named him chief of staff.

Ex-Brazilian President Lula da Silva under investigation

Rousseff said she wanted to bring Lula da Silva into her Cabinet to harness his expertise, 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 the ex-president would effectively be delayed if he were chief of staff.

Brazilian judge blocks Lula appointment – but fight far from over

That appointment prompted massive street protests and a legal battle to block the pick.

The Supreme Federal Court hasn’t ruled yet on whether Lula da Silva can join Rousseff’s Cabinet.

But it decided Thursday that a lower court judge who had been leading the charge in the corruption investigation of the former President doesn’t have jurisdiction. It’s unclear what impact that could have on the case, which is now also in the hands of the Supreme Federal Court.

As the legal battle over Lula da Silva’s case rages, efforts to impeach the President have gained momentum.

The country’s largest political party, the Brazilian Democratic Movement Party, pulled out of Rousseff’s coalition government Tuesday, isolating her politically and prompting her to come out fighting.

“Impeachment without proof of a crime is what? It is a coup,” Rousseff said Wednesday. “There is no point pretending we are discussing a hypothetical impeachment. We are discussing a very concrete impeachment without crime.”

Political woes grow for Rousseff

But the deeply unpopular leader – whose government is weathering approval ratings of around 10% – faces an even greater likelihood of being impeached with the Brazilian Democratic Movement Party’s defection.

The party’s decision for its members to resign their government posts means that Rousseff is unlikely to gather enough votes in the National Congress to avoid impeachment proceedings.

Chris Garman, head of country analysis and managing director at Eurasia Group – a company that analyzes political risk – said his firm estimated Rousseff’s likelihood of being impeached at 60% to 70%. He 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.

Carlos Caicedo, senior analyst for Latin America at analysts IHS, put the likelihood of Rousseff being impeached at about 60%.

“By late December last year we thought that she was going to put this behind her,” he said.

But since the mass demonstrations against her presidency and the police’s questioning of Lula da Silva over the “Car Wash” affair, doing so now looks less likely.

“Those two things together, I think, gave the impetus to the main ally (the Brazilian Democratic Movement Party) to jump ship,” he said.

If impeachment proceedings move forward, they would essentially freeze Rousseff’s government for 180 days while the President fights the efforts.

During that time, a caretaker government would step in – most likely headed by Vice President Michel Temer, leader of the Brazilian Democratic Movement Party and the only member who has not been ordered to step down.

All this uncertainty comes as Brazil grapples with its longest economic downturn since the 1930s.

Already in its second year of recession, the economy is tipped to shrink a further 3.5% this year, according to a pessimistic report Thursday from the Central Bank of Brazil. Previous estimates had predicted a contraction of 1.9%.

Besides battling political troubles, the country 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.

CNN’s Paula Newton, Richard Beltran, Marilia Brocchetto, Flora Charner, Catherine E. Shoichet, Aleks Klosok, Phillipe Vieria, Nina dos Santos and Mayra Cuevas contributed to this report.