Ms. Rousseff does appear to be paying the price for her lack of political experience and skills. An economist by training, she had never held elected public office, serving only in state and federal cabinet posts before Luiz Inácio Lula da Silva, her predecessor, chose her as the Workers Party standard-bearer in the 2010 election. Aided by his popularity, she won handily.

At the peak of the protests last month, Ms. Rousseff made a point of turning to Mr. da Silva, a master of political maneuvering, for advice. But instead of having him fly to Brasília to confer with her, or talking quietly by telephone, she went to meet him on his home turf in São Paulo, leaving the impression among many Brazilians that she was not in charge and he was still pulling the strings.

When they spoke again, he went to Brasília. But unhappiness within the Workers Party, including among members of Congress worried about their own survival in next year’s elections, has fueled speculation in the news media and discussion in the party about Mr. da Silva possibly returning as the party’s candidate if Ms. Rousseff’s downward spiral continued.

“She’s a good head of government and a good administrator, but now she also has to assume the role of leader, and that’s the difficult part,” said Jorge Viana, a senator who is a member of the Workers Party and a supporter of the president. “That’s where we’ve felt the absence of Lula, because Lula is a great leader, with fantastic instincts and a sensitivity for dialogue.”

Ms. Rousseff has had no better luck dealing with the clamor for a political housecleaning than she has had with social demands. In response to public disgust with a political system seen as corrupt and unresponsive — an opinion shared by 81 percent of respondents in a poll published late last month by Datafolha, a leading Brazilian research company — she has offered one ill-fated proposal after another.

After her original idea of a constitutional assembly met with immediate resistance, for example, Ms. Rousseff embraced the idea of a plebiscite. But Congress voted down that proposal last week, in part because of concerns that it would be unconstitutional in the form her government was offering it.