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As an investigation continues into a bribery scandal at Petrobras, protesters gathered on Copacabana Beach in Rio de Janeiro. CreditFelipe Dana/Associated Press 
RIO DE JANEIRO — Hundreds of thousands of protesters took to the streets in cities across Brazil on Sunday to express their ire at President Dilma Rousseff, raising pressure on her as she grapples with an onslaught of challenges including an economy mired in stagnation, a sweeping bribery scandal and a revolt by some of the most powerful figures in her governing coalition.
The protests, organized to coincide with commemorations of the re-establishment of democracy 30 years ago after a long military dictatorship, reflect rising disenchantment with Ms. Rousseff after former executives at Petrobras, the national oil company, revealed an elaborate scheme in which they said they channeled huge bribes from contractors to Ms. Rousseff’s 2010 election campaign, in addition to enriching themselves and legislators supporting her.
The payoff racket coincided roughly with the period that Ms. Rousseff led the company’s board of directors. While no testimony has surfaced claiming that she personally profited from the scheme, calls for her impeachment have been growing louder. Political analysts and even some of Ms. Rousseff’s chief political opponents view impeachment as a distant possibility. Yet with her approval ratings falling sharply, Ms. Rousseff has seen her maneuvering room grow more limited to deal with a range of urgent problems.
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Approval ratings for President Dilma Rousseff, in São Paulo last week, have plummeted.CreditPaulo Whitaker/Reuters 
Concerns are growing over a sluggish economy expected to contract this year as the boom of the previous decade recedes into memory. Brazil’s once-strong currency, the real, has plunged 23 percent against the dollar this year as investors cut their exposure to the economy. Inflation has climbed to its highest level in nearly a decade as job losses mount, partly as a result of the Petrobras scandal rippling through the Brazilian oil industry, which has also been shaken by the worldwide plunge in petroleum prices.
“If there was thievery all around her and they were looting Petrobras, then, yes, the president is responsible,” said Joana Simões Lopes, 40, a fashion designer who was among the protesters in Rio de Janeiro’s seaside Copacabana district. “She should resign simply out of shame.”
Pointing to rising polarization, some prominent supporters of Ms. Rousseff have begun calling supporters of her ouster “golpistas,” or putschists, claiming the movement reflects dissatisfaction among privileged Brazilians rather than broad-based discontent.
But in contrast to leaders elsewhere in the region who have responded to rising dissent by spewing insults at their critics or cracking down with security forces, Ms. Rousseff has taken a relatively nonconfrontational approach. While she has acknowledged the corruption at Petrobras, she contends there is no basis for impeachment.
“In this country, we all have the right to protest,” Ms. Rousseff, 67, said in a video posted over the weekend on her Facebook page in which she alluded to her past as a guerrilla who opposed the dictatorship, which, she noted, harshly restricted civil liberties, including street demonstrations.
Still, the protests are focusing scrutiny on the steady erosion of support for Ms. Rousseff, an economist by training who lacks the talent for political deal-making of her mentor and predecessor as president, Luiz Inácio Lula da Silva. Raising fears about gridlock in Brazil’s Congress, Ms. Rousseff is facing a dispute with the Brazilian Democratic Movement Party, the large centrist party, known as the PMDB, that anchors her coalition.
Leaders of the PMDB, who control both houses of Congress, are fuming after the Supreme Court authorized investigations into claims that they received money from the Petrobras bribery scheme. Blaming Ms. Rousseff for their predicament — the prosecutor general in her government is pursuing the inquiry — they are threatening to block legislation aimed at bolstering unpopular austerity measures.
Beyond the halls of power in the capital, Brasília, a public opinion survey by Datafolha, a Brazilian polling company, showed Ms. Rousseff’s approval ratings declining to 23 percent from 42 percent at the end of 2014. The poll, conducted in early February with interviews of 4,000 people, had a margin of sampling error of plus or minus 2 percentage points.
Brazil’s diverse economy remains on a stronger footing than neighbors like Argentina and Venezuela. A sense of crisis, however, is spreading through the political establishment, which resents Ms. Rousseff’s top-down management style and questions her reluctance to acknowledge that policies expanding the government’s role in the economy might have accentuated some of the problems Brazil faces.
Some political analysts are drawing uneasy comparisons with the turbulent period in the early 1990s, when a corruption scandal moved Fernando Collor de Mello to resign as president in an attempt to thwart his impeachment trial. (He was impeached anyway, shortly after he left office.) Nearly every other civilian president since the 1980s has faced calls for impeachment, but rarely has the momentum built as fast as it has for Ms. Rousseff.
“The protests are an attempt to untie one of the biggest knots of the crisis: the inability of the least-prepared president of the democratic era to deal with the most difficult process Brazil is facing in the last 30 years,” said Fernando Gabeira, a respected writer and founder of Brazil’s Green Party.
Still, Ms. Rousseff and the governing Workers Party still command important bastions of support. Many Brazilians who have climbed out of poverty in recent years, partly because of the government’s social welfare programs, remain loyal to Ms. Rousseff, who narrowly won re-election last October.
“There is no evidence for removing Dilma from the presidency, so let her finish her term,” said Kelly Molina Porto, 33, a street vendor who attended smaller protests on Friday here in support of the president. “She was democratically elected.”
At the same time, others are saying they have had enough after witnessing the evolution of the leftist Workers Party from an insurgent organization that criticized the rampant corruption in Brazil’s political system into an establishment fixture, fending off accusations that it benefited from what may be the largest bribery scandal in the country’s history.
“The economy is entirely for them, and they don’t care if this finishes with Brazil,” said Laerte Alves Machado, 61, a civil engineer among the protesters in São Paulo, referring to the Workers Party. “They just want to stay in power.”